Integral with Simpson's_rule

Simpson.c

#include <stdio.h>		// printf
#include <math.h>		// sin, atan

double simpson(double a, double b, double (*func)(double));	// Simpson's_rule
double integral(double xi, double xf, int n, double (*func)(double));	// Integral with some tools

int main() {
	double pi =  4.0*atan(1.0);
	double surface;
	for (int i=10; i<=50; i+=2) {
		surface = integral(0.0, pi, i, sin);
		printf("N = %d, Surface = %.22lf \n", i, surface);
	}

	return 0;
}


double simpson(double a, double b, double (*func)(double)){
	double f = func(a) + 4*func((a+b)/2) + func(b);
	f *= (b-a)/6;
	return f;
}

double integral(double xi, double xf, int n, double (*func)(double)){
	double xStep = (xf-xi)/n;
	double surface = 0.0;
	double x1, x2;
	for (int i=0; i<n; ++i) {
		x1 = xStep * i;
		x2 = xStep * (i+1);
		surface += simpson(x1, x2, func);
	}
	
	return surface;
}