The study over the period of 8 weeks begins with a introduction to integral equations,their types that is Volterra and Fredholm,their various methods of solutions including exact, approximate and numerical methods of solutions.Finally,the study turns to different techniques that could be used to approximate the solutions at different points within the given range.In this,the exact solution is obtained using the appropriate method as the selection was done in such a way that the exact solution was available and then again a method was applied to get the approximate solution.Finally the two values obtained were compared.The computations were done using a software Mathematica(version 7).