Функция вычисляющая интеграл методом средних прямоугольников

#include <iostream>
#include <cmath>
#define _USE_MATH_DEFINES
using namespace std;
double integral(double (*func) (double), double a, double b) {
    int n = 1000;
    double h = (b - a) / n;
    double s = 0.0;
    for (double i = a; i < b - h / 2; i += h)
    {
        s += func(i + (h / 2)) * h;
    }
    return s;
}
double func(double x) {
    return (sin(x) * log(tan(x)));
}
double coolintegral(double (*func) (double), double a, double b, int n) {
    double h = (b - a) / n;
    double s = 0.0;
    for (double i = a; i < b - h / 2; i += h)
    {
        s += func(i + (h / 2)) * h;
    }
    return s;
}
int main()
{
    double a = 1.;
    double b = 1.5;
    int n = 0;  
    double f = -log(abs(1/sin(b)+1/tan(b)))-cos(b)*log(tan(b))+ log(abs(1 / sin(a) + 1 / tan(a)))+ cos(a) * log(tan(a));
    cout << "Newton - Leibniz Formula: " << f << endl;
    f = integral(func, a, b);
    cout << "The method of average rectangles: " << f << endl;
    cout << "Vvedite kol-vo razbieniy" << endl;
    while (n == 0)cin >> n;
    f = coolintegral(func, a, b, n);
    cout << "The method of SUPER average rectangles: " << f << endl;
    system("pause");
}