程序代码：

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <conio.h>

double Integral(double low, double high, double increase, double (*Func)(double));
double Func1(double x);
double Func2(double x);
double Func3(double x);

const double Increase = 0.0001;

int main(void)
{
    printf_s("f(x) = x^3 +3x^2 - x + 4   在 (0,1)上的定积分 = %f\n", Integral(0.0, 1.0, Increase, Func1));
    printf_s("f(x) = x * sqrt(1 + cos2x) 在 (0,1)上的定积分 = %f\n", Integral(0.0, 1.0, Increase, Func2));
    printf_s("f(x) = 1 / (1 + x^2)       在 (0,1)上的定积分 = %f\n", Integral(0.0, 1.0, Increase, Func3));

    _getch();
    return EXIT_SUCCESS;
}

// 求任意函数的定积分
double Integral(double low, double high, double increase, double (*Func)(double))
{
    double integral = 0.0;

    for (double x = low; x <= high; x += increase)
    {
        integral += Func(x) * increase;
    }

    return integral;
}

// f(x) = x^3 + 3x^2 - x + 4
double Func1(double x)
{
    return pow(x, 3) + 3 * pow(x, 2) - x + 4;
}

// f(x) = x * sqrt(1 + cos2x)
double Func2(double x)
{
    return x * sqrt(1 + cos(2 * x));
}

// f(x) = 1 / (1 + x^2)
double Func3(double x)
{
    return 1 / (1 + pow(x, 2));
}