The program willl not compile and need to get the correct integral solution. In compiler there is no errors present.

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C

cannot get the code to run. objective is to solve the program for function 1 being x^2 function 2 being sin(x^2) and function 3 being sin(x^2). Calculate parameters being deltax is equal to .0001. Program should be an integral calculator.

Bounds is pi = b(top bound) 0=a (lower bound) for f(x) = sin(x) and deltax = .0001
$ ./integral 1 0 3.1415926 0.0001
integral value = 2.000000


Bounds is 2 = b(top bound) 0=a (lower bound) for f(x) = (x^2) and deltax = .0001
$ ./integral 2 0 2 0.0001
integral value = 2.666667

What I have tried:

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define PI 3.14159265
double factorial(unsigned int n)
{
    double result;
    if (n == 0) {
        return 1;
    }
  
    result = n*factorial(n-1);
    return result;
}
double power(double num, int n)
{
  double result = 1.0;
  double stable = num;
  for(int i=1; i<n+1; i++)
  {
    result = result * stable;
  }
  return result;

}

double functionOne(double a, double b, double delta)
{
    double answer = 0;
    int i;
    int sign = 1;

        
    for (i=a; i<=b; i+= delta) {
		double xterm = (pow(b,3)-pow(a,3))/3;
        double nfact = factorial(i);
		sign = sign * -1;	// flip sign from 1 to -1 and vice versa
		answer = answer + sign*xterm/nfact;
    }

    return answer;
}

double functionTwo(double a, double b)
{
 double answer = (pow(b,3)-pow(a,3))/3;

  return answer;
 
}

double functionThree(double a, double b, double delta)
{
    double answer = 0;
    int i;
    int sign = 1;

        
    for (i=a; i<=b; i+= delta) {
		double xterm = (pow(b,3)-pow(a,3))/3;
        
		sign = sign * -1;	// flip sign from 1 to -1 and vice versa
		answer = answer + sign*xterm;
    }

    return answer;
}
int main(int argc, char **argv) 
{
  double select = atof(argv[1]);
  double a = atof(argv[2]);
  double b = atof(argv[3]);
  double delta =  atof(argv[4]);
  
  
  if(select == 1)
  {
    double answer = functionOne(a,b,delta);
    printf("integral value is: %f\n", answer);
  }
  else if(select == 2)
  {
    double answer = functionTwo(a,b);
    printf("integral value is: %f\n", answer);
  }
  else if(select == 3)
  {
    double answer = functionThree(a,b,delta);
    printf("integral value is: %f\n", answer);
  }
  
}