Do Simple Calculus in Java

The Java class below is for doing simple calculus. Method "private double differentiate(double x)" is used to differentiate the function at x, and method "private double integrate(double from, double to)" is used to integrated the function between from and to.

import javax.swing.JOptionPane;

public class SimpleCalculus {

 public interface CalculusInterface {
  public double function(double x);
 }
 
 private CalculusInterface calculusInterface;
 public SimpleCalculus(CalculusInterface calculusInterface){
  this.calculusInterface = calculusInterface;
 }
 
 private double integrate(double from, double to) {
  final int intevalNum = 1000000;
  double inteval = (to - from) / intevalNum;
  double result = 0d;
  for (int i = 0; i < intevalNum; i++) {
   try {
    result += (calculusInterface.function(from + i*inteval) + 
      calculusInterface.function(from + (i + 1)*inteval)) * inteval / 2;
    
   } catch (Exception e) {
    // TODO: handle exception
    JOptionPane.showMessageDialog(null, "The function is not integrable 
    between " + from + " and " + to);
    System.exit(0);
   }
  }

  return result;
 }
 
 private double differentiate(double x){
  final double aSmallValue = 0.0000000001;
  try {
   double d1 = (calculusInterface.function(x + aSmallValue) - 
     calculusInterface.function(x))/(aSmallValue);
   double d2 = (calculusInterface.function(x - aSmallValue) - 
     calculusInterface.function(x))/( - aSmallValue);
   double ratio = d1/d2;
   if (ratio > 1.01 || ratio < 0.99){
    JOptionPane.showMessageDialog(null, "The function is not differntiable at " + x);
    System.exit(0);
   }
   return (d1 + d2) / 2; 
  } catch (Exception e) {
   // TODO: handle exception
   JOptionPane.showMessageDialog(null, "The function is not differntiable at " + x);
   System.exit(0);
   return 0;
  }
 }

 public static void main(String[] args) {
  SimpleCalculus calculus = new SimpleCalculus(new CalculusInterface() {
   @Override
   public double function(double x) {
    //the function to be integrated or differentiated; configure it on your own
    return x * x;
   }
  });
  
  double integrationValue = calculus.integrate(0, 2);
  System.out.println("Integration value is : " + integrationValue);
  double differentiationValue = calculus.differentiate(1);
  System.out.println("Differentiation value is : " + differentiationValue);
  
 }

}