java - Riemann Integrator Sum Issue -

here code riemann integrator:

public class riemannintegrator {      public static void main (string [] args)     {         double lower = double.parsedouble(args[args.length -2]);         double higher = double.parsedouble(args[args.length -1]);          double[] coefficients = new double[args.length - 3];          if (args[0].equals("poly"))         {             (int = 1; < args.length - 2; i++)             {                 coefficients[i-1] = double.parsedouble(args[i]);             }              system.out.println(integral("poly", coefficients, lower, higher));         }     }      private static double integral(string s, double[] function, double lowbound, double highbound)     {          double area = 0; // area of rectangle         double sumofarea = 0; // sum of area of rectangles         double width = highbound - lowbound;               if (s.equals("poly"))             {                 (int = 1; <= ((highbound - lowbound) / width); i++) // represents # of rectangles                 {                     system.out.println("rectangles:" + i);                     (int j = 0; j < function.length; j++) // goes through coefficients                     {                            area = width * function[j] * math.pow ( (double)( (i * width + lowbound + (i -1.0) * width + highbound) / 2.0 ),function.length- 1- j);                           /*above code computes area of each rectangle */                          sumofarea += area;                     }                 }             }             width = width / 2.0;             system.out.println("polynomial, function (of length), lower boundary, higher boundary.");             function.tostring();             system.out.println("lower bound:" + lowbound + ", higher bound: " + highbound + ".");             system.out.println("the integral is:");             return sumofarea;     }    } 

it works part, however, math wrong more not, , don't know went wrong. example, if want find sum of function of x^3+2x^2+3x, 2.416667 on calculator, , on wolfram alpha. but, in program, tells me 6. think may have number of rectangles, because tells me 1 rectangle. can help?

you need loop, along lines of

double width = highbound - lowbound; double epsilon = .001; // determines how accurate want solution be, closer 0 = more accurate double prevvalue = -1.0; double curvalue = -1.0; // initialize curvalue negative value greater magnitude epsilon - ensures while loop evaluates true on first pass {     ... // loop goes     prevvalue = curvalue;     curvalue = sumofarea;     width /= 2.0; } while(math.abs(prevvalue - curvalue) > epsilon); 

the idea keep decreasing rectancles' width until sumofarea width = w more-or-less same (i.e. within epsilon) sumofarea width = 2w.

there faster + more accurate integration algorithms out there e.g. newton-cotes, i'm assuming don't have choice in matter.