Does Simpsons rule still apply when a < 0?

Question

I am currently working on an assignment where I have to find the answer to the following integral using Simpsons rule:$\int x+1$ (MIN = -1 MAX = 3), I choose to have 6 intervals. I now start calculating: $delta X = \frac{b-a}{n} = \frac{3--1}{6} = \frac{4}{6} = 0.6666666~$ $$\frac{\frac{6}{4}}{3} (=>\frac{2}{9})*(f(0*\frac{4}{6} + 4* f(1*\frac{4}{6})+ 2* f(2*\frac{4}{6})+ 4* f(3*\frac{4}{6})+ 2* f(4*\frac{4}{6})+ 4* f(5*\frac{4}{6}) + f(6*\frac{4}{6})) = \frac{34}{3} = 11.3333$$ (The actual calculation was done by wolfram alpha)It should be 8. I wrote this into a Java funtion:

public class Simpsons_rule {
public void start(Formula f, int n) throws Exception{
    if (n%2 != 0){
        throw new Exception("n must be even.");
    }        
    double deltaX = (f.getB() - f.getA())/n;
    double endanswer = 0.0;
    for (double interval = 1.0; interval < n ; ++interval){
        if (interval%2 != 0){
            endanswer += 4*(f.calculate(interval * deltaX));
        } else {
            endanswer += 2*(f.calculate(interval * deltaX));
        }
    }
    endanswer += f.calculate(0); //or 0*deltaX, whichever you prefer
    endanswer += f.calculate(n*deltaX));
    endanswer *= deltaX/3;
    System.out.println(endanswer);
}

}

The class that gets used:

public class Som3 implements Formula {

    @Override
    public void print() {
        System.out.println("Som 3\n x+1 dx (MIN = -1 MAX = 3");
    }

    @Override
    public double calculate(double d) {
        return d+1;
    }

    @Override
    public double getA() {
        return -1;
    }

    @Override
    public double getB() {
        return 3;
    }

    @Override
    public void printCorrectAnswer() {
        System.out.println("The correct answer: 8 (Calculated by Wolfram Alpha)");
    }

}

This function works perfect for any intergral that I push into it, except for this one. The only difference between these intergrals is that a is below 0 here and above or equal to zero everywhere else. Is it true that Simpsons rule only applies when a>=0? Or Am I doing something wrong?

Edit: My understanding of Simpsons rule was incorrect, here is the correct version of class Simpsons_Rule:

public class Simpsons_rule {
    public void start(Formula f, int n) throws Exception{
        if (n%2 != 0){
            throw new Exception("n must be even.");
        }        
        double deltaX = (f.getB() - f.getA())/n;
        double endanswer = 0.0;
        for (double interval = 1.0; interval < n ; ++interval){
            if (interval%2 != 0){
                endanswer += 4*(f.calculate(interval * deltaX + f.getA()));
            } else {
                endanswer += 2*(f.calculate(interval * deltaX + f.getA()));
            }
        }
        endanswer += f.calculate(f.getA()); //or 0*deltaX, whichever you prefer
        endanswer += f.calculate(f.getB());
        endanswer *= deltaX/3;
        System.out.println(endanswer);
    }

}

Answer 1

I would not use a double for interval, but regarding your question: $a<0$ is allowed, all you should require is $b>a$.

However, why do you call f.calculate(0) and not f.calculate(f.getA())? Or maybe you should call f.calculate(f.getB()-f.getA()) instead of f.calculate(f.getB())? It is hard to tell without knowing what calculate does. At any rate, I suspect that your method fails for many functions and intervals.