Trying to get the correct output!!!!

[bruntmjust]

#include <iostream>
#include <cmath>

using std::cin;
using std::cout;
using std::endl;

double func_1(double);
double func_2(double);
double func_3(double);
double func_4(double);
double func_5(double);
double rect_integral(double a, double b, int n, int choice);
double trap_integral(double a, double b, int n, int choice);

const char * funcname[6] = {
    "",
    "5x^4 + 3x^3 - 10x + 2",
    "x^2 - 10",
    "40x + 5",
    "x^3",
    "20x^2 + 10x - 2" };

int main () {

    int choice;
    int n;
    double a;
    double b;
    double h;
    double x;
    double area;
    bool trap = false;
    bool rect = false;

    cout << "Functions available: \n\n";
    for (int i=1; i<6; i++)
        cout << "  " << i << "  " << funcname[i] << '\n';
        cout << endl;

        cout << "Choose a function (1, 2, 3, 4, 5, other(quit)) " << endl;
        cin >> choice;

        if (choice >= 1 && choice <= 5)
        {
           char method = ' ';
           do {
               cout << "Would you like to calculate the area using the rectangle,"
                 << " trapezoid, or both (1, 2, 3): " << endl;
               cin >> method;
        } while (method < '1' || method > '3');

        switch (method) {
            
                case '1':
                rect = true;
                cout <<"How many rectangles do you want? " << endl;
                break;
                
                case '2':
                trap = true;
                cout <<"How many trapezoids do you want? " << endl;
                break;
                
                case '3':
                trap = true;
                rect = true;
                cout <<"How many rectangles/trapezoids do you want? " << endl;
        }

        cin >> n;

        cout <<"Please select a starting point, a: " << endl;
        cin >> a;

        cout <<"Please select an ending point, b: " << endl;
        cin >> b;

        if (rect) {
            cout << "The area under " << funcname[choice]
                 << " between " << a << " and " <<  b
                 << " is: " <<  rect_integral(a, b, n, choice) << endl;
        }

        if (trap) {
            cout << "The area under " << funcname[choice]
                 << " between " << a << " and " <<  b
                 << " is: " <<  trap_integral(a, b, n, choice) << endl;
        }
    }

    return 0;
}

double func_1 (double x)
{
    return 5.0*x*x*x*x + 3.0*x*x*x - 10.0*x + 2.0;
}

double func_2 (double x)
{
    return x*x - 10.0;
}

double func_3 (double x)
{
    return 40.0*x + 5;
}

double func_4 (double x)
{
    return x*x*x;
}

double func_5 (double x)
{
    return 20.0*x*x + 10.0*x - 2.0;
}

double rect_integral(double a, double b, int n, int choice)
{
    // here insert the code to calculate the integral
    return 1.0; // dummy value
}

double trap_integral(double a, double b, int n, int choice)
{
    // here insert the code to calculate the integral
    return 2.0; // dummy value
}

this code compiles but I need to get the program to do this:

Choose a function (1, 2, 3, 4, 5, other(quit)): 1
Would you like to calculate the area using the rectangle, trapezoid, or both (1, 2, 3): 2
How many trapezoids do you want? 1000
Please select a starting point, a = 1
Please select an ending point, b = 2
The area under 5x4 + 3x3 – 10x + 2 between 1 and 2 is 29.25

I need the program to output 29.25 but I cant figure out what to. Help please. help with code!

[bruntmjust]

And here is some more information:

n = number of rectangles and/or trapezoids
a = beginning x value
b = ending x value
h = width of each rectangle/trapezoid, (b-a)/n
f(x) = height of rectangle
(f(x1)+f(x2))/2 = height of trapezoid
Area = width*height

Integration Program Definition: Your program should determine the area under these different functions,
f1(x) = 5x4 + 3x3 – 10x + 2
f2(x) = x2 – 10
f3(x) = 40x + 5
f4(x) = x3
f5(x) = 20x2 + 10x – 2