diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/functionTypes.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/functionTypes.kt
new file mode 100644
index 000000000..788f8bc53
--- /dev/null
+++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/functionTypes.kt
@@ -0,0 +1,7 @@
+package space.kscience.kmath.functions
+
+import space.kscience.kmath.structures.Buffer
+
+public typealias UnivariateFunction<T> = (T) -> T
+
+public typealias MultivariateFunction<T> = (Buffer<T>) -> T
\ No newline at end of file
diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/GaussIntegrator.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/GaussIntegrator.kt
index d58b6131f..a4f79f542 100644
--- a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/GaussIntegrator.kt
+++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/GaussIntegrator.kt
@@ -23,7 +23,7 @@ import space.kscience.kmath.structures.indices
 /**
  * A simple one-pass integrator based on Gauss rule
  */
-public class GaussIntegrator<T : Any> internal constructor(
+public class GaussIntegrator<T : Comparable<T>> internal constructor(
     public val algebra: Ring<T>,
     private val points: Buffer<T>,
     private val weights: Buffer<T>,
@@ -31,6 +31,7 @@ public class GaussIntegrator<T : Any> internal constructor(
 
     init {
         require(points.size == weights.size) { "Inconsistent points and weights sizes" }
+        require(points.indices.all { i -> i == 0 || points[i] > points[i - 1] }){"Integration nodes must be sorted"}
     }
 
     override fun integrate(integrand: UnivariateIntegrand<T>): UnivariateIntegrand<T> = with(algebra) {
@@ -54,12 +55,13 @@ public class GaussIntegrator<T : Any> internal constructor(
             range: ClosedRange<Double>,
             numPoints: Int = 100,
             ruleFactory: GaussIntegratorRuleFactory<Double> = GaussLegendreDoubleRuleFactory,
+            features: List<IntegrandFeature> = emptyList(),
             function: (Double) -> Double,
-        ): Double {
+        ): UnivariateIntegrand<Double> {
             val (points, weights) = ruleFactory.build(numPoints, range)
             return GaussIntegrator(DoubleField, points, weights).integrate(
                 UnivariateIntegrand(function, IntegrationRange(range))
-            ).value!!
+            )
         }
     }
 }
\ No newline at end of file
diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/GaussIntegratorRuleFactory.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/GaussIntegratorRuleFactory.kt
index 234859991..a3adacc04 100644
--- a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/GaussIntegratorRuleFactory.kt
+++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/GaussIntegratorRuleFactory.kt
@@ -1,6 +1,7 @@
 package space.kscience.kmath.integration
 
 import space.kscience.kmath.operations.DoubleField
+import space.kscience.kmath.operations.Field
 import space.kscience.kmath.operations.Ring
 import space.kscience.kmath.structures.*
 import kotlin.jvm.Synchronized
@@ -8,7 +9,7 @@ import kotlin.math.ulp
 import kotlin.native.concurrent.ThreadLocal
 
 public interface GaussIntegratorRuleFactory<T : Any> {
-    public val algebra: Ring<T>
+    public val algebra: Field<T>
     public val bufferFactory: BufferFactory<T>
     public fun build(numPoints: Int): Pair<Buffer<T>, Buffer<T>>
 
@@ -29,7 +30,7 @@ public fun <T : Comparable<T>> GaussIntegratorRuleFactory<T>.build(
     val points = with(algebra) {
         val length = range.endInclusive - range.start
         normalized.first.map(bufferFactory) {
-            range.start + length * it
+            range.start + length / 2 + length * it/2
         }
     }
 
@@ -46,7 +47,7 @@ public fun <T : Comparable<T>> GaussIntegratorRuleFactory<T>.build(
 @ThreadLocal
 public object GaussLegendreDoubleRuleFactory : GaussIntegratorRuleFactory<Double> {
 
-    override val algebra: Ring<Double> get() = DoubleField
+    override val algebra: Field<Double> get() = DoubleField
 
     override val bufferFactory: BufferFactory<Double> get() = ::DoubleBuffer
 
diff --git a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/UnivariateIntegrand.kt b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/UnivariateIntegrand.kt
index 637761497..9d515e754 100644
--- a/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/UnivariateIntegrand.kt
+++ b/kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/UnivariateIntegrand.kt
@@ -1,12 +1,13 @@
 package space.kscience.kmath.integration
 
+import space.kscience.kmath.functions.UnivariateFunction
 import space.kscience.kmath.misc.UnstableKMathAPI
 import kotlin.jvm.JvmInline
 import kotlin.reflect.KClass
 
 public class UnivariateIntegrand<T : Any> internal constructor(
     private val features: Map<KClass<*>, IntegrandFeature>,
-    public val function: (T) -> T,
+    public val function: UnivariateFunction<T>,
 ) : Integrand {
 
     @Suppress("UNCHECKED_CAST")
diff --git a/kmath-functions/src/commonTest/kotlin/space/kscience/kmath/integration/GaussIntegralTest.kt b/kmath-functions/src/commonTest/kotlin/space/kscience/kmath/integration/GaussIntegralTest.kt
new file mode 100644
index 000000000..7c33ea73f
--- /dev/null
+++ b/kmath-functions/src/commonTest/kotlin/space/kscience/kmath/integration/GaussIntegralTest.kt
@@ -0,0 +1,30 @@
+package space.kscience.kmath.integration
+
+import kotlin.math.PI
+import kotlin.math.sin
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+class GaussIntegralTest {
+    @Test
+    fun gaussSin() {
+        val res = GaussIntegrator.integrate(0.0..2 * PI) { x ->
+            sin(x)
+        }
+        assertEquals(0.0, res.value!!, 1e-4)
+    }
+
+    @Test
+    fun gaussUniform() {
+        val res = GaussIntegrator.integrate(0.0..100.0,300) { x ->
+            if(x in 30.0..50.0){
+                1.0
+            } else {
+                0.0
+            }
+        }
+        assertEquals(20.0, res.value!!, 0.1)
+    }
+
+
+}
\ No newline at end of file