Why do we use these quadrature methods, if we can already integrate using formulae?? This is a basic question that must be answered, and the answer to it is simple. We use these methods to find the integral within limits of the functions which are not easily integratable or just don't give a result by general integration methods, many examples can be found easily and on google simply so i'll not insert them here. So, to solve these integrals which don't give a solution by general methods easily we use methods like integration using trapezoids, simpson's method and gauss quadratures. Hope u learnt something new today.