title: How to compute integration of a function in apache commons math3 library?
body: <p>I am trying to integrate a very simple function. integral(x.dx). Instead of getting an answer of 1, I am getting an answer as 0, or 0.5 when I include limits from 0 to 1. Is there something I misunderstand about the implementation of the integration in apache commons library?</p>
  
  <pre><code>import org.apache.commons.math3.analysis.integration.*;
  import org.apache.commons.math3.analysis.polynomials.*;
  
  public static void main(String args[])
  {
      SimpsonIntegrator simpson = new SimpsonIntegrator();
      TrapezoidIntegrator trapezoid = new TrapezoidIntegrator();
      double[] vector = new double[2];
      vector[0] = 0;
      vector[1] = 1;
  
      PolynomialFunction f = new PolynomialFunction(vector);
      UnivariateFunction uf = (UnivariateFunction)new PolynomialFunction(vector);
      System.out.println("To String " + uf.toString());
      System.out.println("Degree: " + f.degree());
  
      double i = simpson.integrate(10, uf, -Float.MAX_VALUE, Float.MAX_VALUE);
      double j = trapezoid.integrate(10, uf, 0, 1);
      System.out.println("Simpson integral : " + i);        
      System.out.println("Trapezoid integral : " + j);        
  }
  /*** OUTPUT 
  To String x
  Degree: 1
  Simpson integral : 0.0
  Trapezoid integral : 0.5
  ***/
  </code></pre>