public static double partitionSumIterativ(double epsilon, double a, double b) {
    int n = 0;
    double c = b;
    while(c-a > epsilon) {
        n++;
        c = a + (c-a)/2;
    }

    double area = 0;
    double h = (b-a)/n;
    for(int i = 0; i < n; i++) {

        area += h * (-0.25 * a * a + 4);
        a = a + h;
        b = b - h;
    }

    return area;
}

public static double partitionSum(double epsilon, double a, double b) {

    //Some code to calculate n

    double h = (b-a)/n;
    double area = h * (-0.25 * a * a + 4) + partitionSum(epsilon, a', b'); //Where a' is a new a and b' is a new b (please see Questions below)

    return area;
}