A large number of real definite integrals whose evaluation by usual methods is sometimes very tedious can be easily evaluated by using Cauchy’s residue theorem. The main objective of this chapter is to discuss and demonstrate the evaluation of definite integrals by using the techniques of the calculus of residues. From a generalized point of view, several definite integrals which would require highly adhoc techniques for their evaluation are treated easily by this technique, which lends at once a high degree of unification and extension to the knowledge of definite integrals.