public class Calculus
{
    public static double integrate(double lowerBound, double upperBound, int numRec)
    {
        double area = 0.0;
        
        double base = (upperBound - lowerBound) / numRec;
        for(double midpoint = base / 2 + lowerBound; midpoint < upperBound; midpoint += base)
        {
            area += base * function(midpoint);
        }
        
        return area;
    }
    
    private static double function(double x)
    {
        return x * x;
    }
}