矩形积分：
#include<iostream>                                    //???????结果不对？？？？？？？
#include<fstream>
#include<cmath>
using namespace std;
//--------------------
double g(double x);
double rectangle(double a,double b,double(*f)(double));
//---------------------------------------------------------
int main()
{
    ifstream in("integral.txt");
    cout<<fixed;
    cout.precision(3);
    for(double b;in>>b;)
        cout<<rectangle(1,b,g)<<endl;                        
}
//------------------------------
double g(double x)
{
    return 1/x;
}
//-------------------------
double rectangle(double a,double b,double(*f)(double))
{
    long double w=b-a,sumnew=w*(f(a)+f(b))/2,sumold=0;
    for(int n=1;fabs(sumnew-sumold)>=1e-4;n*=2)               
    {
        sumold=sumnew;
        sumnew=0;
        for(int i=0;i<n;++i)                                
        {
            sumnew+=f(a+w*(i+0.5)/n);                    //共n个小矩形时第i个矩形的中间位置坐标a+w*(i+0.5)/n
            sumnew*=w/n;                                //切割第n次宽度为w/n
        }
        return    sumnew;
    }
}
辛普生积分：
#include<iostream>
#include<fstream>
#include<cmath>
using namespace std;
//--------------------
double g(double x);
double simpson(double a,double b,double(*f)(double));
//---------------------------------------------------------
int main()
{
    ifstream in("integral.txt");
    cout<<fixed;
    cout.precision(9);
    for(double b;in>>b;)
        cout<<simpson(1,b,g)<<endl;                        //第三个参数为函数指针！！！
}
//------------------------------
double g(double x)
{
    return 1/x;
}
//-------------------------
double simpson(double a,double b,double(*f)(double))
{
    double h=b-a,t2=h*(f(a)+f(b))/2,t1,i1=t2,i2=0;            //i1老积分，i2新积分。
    for(int n=1;fabs(i1-i2)>=1e-4;n+=n,h/=2.0)                    
    {
        t1=t2;i1=i2;
        double sigma=0;                                        //sigma=0初值        
        for(int i=0;i<n;++i)                                
            sigma+=f(a+h*(i+0.5));                            //共n个小矩形时第i个矩形的中间位置坐标a+w*(i+0.5)/n
        t2=(t1+sigma*h)/2;                                //切割第n次宽度为w/n
        i2=(4*t2-t1)/3;
        return    i2;
    }
}

integral。txt：
3
27.64738
0.0493
0.99954
0.0000557
100001
书上结果是：
1.099
3.320
-3.010
-0.000
-9.767
11.513