The fundamental theorem of calculus states that the de?nite integral of a function may be found from the antiderivative of the function. However, for many functions, it is much easier to show that they have a de?nite integral than it is to ?nd an expression for the antiderivative in terms of elementary functions. Several numerical techniques for ?nding de?nite integrals are based on approximating the function to be integrated by a simpler function whose antiderivative can be found exactly. The accuracy of approximate integral depends on the form of the approximating function and the number of functions evaluations. The basic numerical methods for integration may be improved by subdividing the interval of integration and using the fact that the integral over the entire interval is the sum of the integrals over the subintervals, these are known as composite numerical integration methods. Let us start with the basic numerical integration and then introduce the composite methods later on. You should monitor the accuracy to see how much one gains by using composite methods.