diff --git a/src/main/java/org/apache/commons/math3/analysis/integration/MidPointIntegrator.java b/src/main/java/org/apache/commons/math3/analysis/integration/MidPointIntegrator.java
index 059af63eb..8058b6aa3 100644
--- a/src/main/java/org/apache/commons/math3/analysis/integration/MidPointIntegrator.java
+++ b/src/main/java/org/apache/commons/math3/analysis/integration/MidPointIntegrator.java
@@ -120,7 +120,7 @@ public class MidPointIntegrator extends BaseAbstractUnivariateIntegrator {
         final double diff = getMax() - min;
 
         if (n == 0) {
-            final double midPoint = 0.5 * diff;
+            final double midPoint = min + 0.5 * diff;
             return diff * computeObjectiveValue(midPoint);
         } else {
             final long np = 1L << (n - 1);           // number of new points in this stage
diff --git a/src/test/java/org/apache/commons/math3/analysis/integration/MidPointIntegratorTest.java b/src/test/java/org/apache/commons/math3/analysis/integration/MidPointIntegratorTest.java
index d0a5fa9c8..928817681 100644
--- a/src/test/java/org/apache/commons/math3/analysis/integration/MidPointIntegratorTest.java
+++ b/src/test/java/org/apache/commons/math3/analysis/integration/MidPointIntegratorTest.java
@@ -35,6 +35,25 @@ import org.junit.Test;
  */
 public final class MidPointIntegratorTest {
 
+    /**
+     * Test of integrator for the sine function.
+     */
+    @Test
+    public void testLowAccuracy() {
+        UnivariateFunction f = new QuinticFunction();
+        UnivariateIntegrator integrator = new MidPointIntegrator(0.01, 1.0e-10, 2, 4);
+        
+        double min = -10;
+        double max =  -9;
+        double expected = -3697001.0 / 48.0;
+        double tolerance = FastMath.abs(expected * integrator.getRelativeAccuracy());
+        double result = integrator.integrate(Integer.MAX_VALUE, f, min, max);
+        Assert.assertTrue(integrator.getEvaluations() < Integer.MAX_VALUE / 2);
+        Assert.assertTrue(integrator.getIterations() < MidPointIntegrator.MIDPOINT_MAX_ITERATIONS_COUNT / 2);
+        Assert.assertEquals(expected, result, tolerance);
+
+    }
+
     /**
      * Test of integrator for the sine function.
      */