C#: How to perform Numerical Integration

gistfile1.cs

using System;

namespace NumericalIntegration {
    class Program {
        static void Main(string[] args) {
            int iterations = 100000;
            double x, start, end, dist, sum = 0, sumT = 0;
            
            Console.Write( "Input range start: " );
            start = double.Parse( Console.ReadLine() );
            
            Console.Write( "Input range end: " );            
            end = double.Parse( Console.ReadLine() );

            dist = ( end - start ) / iterations;

            for ( int i = 1 ; i <= iterations ; i++ ) {
                x = start + i * dist;
                sumT += f( x - dist / 2 );

                if ( i < iterations ) {
                    sum += f( x );
                }
            }
            
            sum = ( dist / 6 ) * ( f( start ) + f( end ) + 2 * sum + 4 * sumT );            
            Console.WriteLine( "Value on range [{0}, {1}] is around: {2}", start, end, sum );

            Console.Read();
        }

        private static double f(double x) {
            return Math.Sin(x);
        }

    }
}