Simple rectangle method algorithm problem

Question

I've been asked to write a rectangle method algorithm to calculate estimated area of function, however, my lecturer sent my code back and asked me to correct it, because ending condition is wrong?

double prostokaty(double( *f)(double))
{
    double krok, p, suma = 0;
    krok = (c_do - c_od) / lp;
    for (p = c_od + krok; p < c_do; p += krok) {
        suma += (*f)(p);
    }
    return suma * krok;      
}

I've spent almost two hours, figuring out whats wrong and I failed.

Answer 1

Better to use the middle c_od + krok/2 of the rectangle rather than the right edge c_od + krok.

double prostokaty(double( *f)(double)) {
  double p, suma = 0;
  double krok = (c_do - c_od) / lp;
  // for (p = c_od + krok; p < c_do; p += krok) {
  for (p = c_od + krok/2; p < c_do; p += krok) {
    suma += (*f)(p);
  }
  return suma * krok;      
}

If lp is an integer type, better to avoid accumulated increment errors.

  double suma = 0;
  double krok = (c_do - c_od) / lp;
  for (int i = 0; i < lp; i++) {
    double p = c_od + (i + 0.5)*krok;
    suma += f(p);
  }
  return suma * krok;