definite integral

#include <math.h>
#include <stdio.h>
int main(void) {
  puts("maxN   A        A2     |A-A2|");
  puts("------------------------------");
  int n, maxN;
  double A, A2, x0 = 0.;
  double xn = M_PI_4;
  double x, dx;
  maxN = 1;
  while (maxN <= 100) {
    dx = (xn - x0) / maxN;
    A = A2 = 0.;
    for (n = 0; n <= maxN - 1; n = n + 1) {
      x = x0 + n * dx;
      A = A + x * sin(x) * dx;
      A2 = A2 + (x * sin(x) + (x + dx) * sin(x + dx)) * dx / 2.;
    }
    if (!(maxN % 10)) { printf("%3d %f %f %f\n", maxN, A, A2, fabs(A - A2)); }
    maxN = maxN + 1;
  }
  return 0;
}