To make effective use of integration it is necessary to develop a systematic approach to the integration of standard forms of integral. This is accomplished in this chapter, which discusses integration by substitution, integration by parts, the use of reduction formulae and the use of partial fractions to simplify the task of integrating rational functions. It is shown how these same techniques may be used to find antiderivatives (indefinite integrals) which are just functions, and definite integrals which are numbers. The chapter ends with a discussion of differentiation under the integral sign and the integration of trigonometric functions involving multiple angles.