A heuristic computer program for the evaluation of real definite integrals of elementary functions is described. This program, called WANDERER (WANg's DEfinite integRal EvaluatoR), evaluates many proper and improper integrals. The improper integrals may have a finite or infinite range of integration. Evaluation by contour integration and residue theory Is among the methods used. A program called DELIMITER (DEfinitlve LIMIT
EvaluatoR) is used for the limit computations needed in evaluating some definite integrals. DELIMITER is a heuristic program written for computing limits of real or complex analytic functions. For real functions of a real variable, one-sided as well as two-sided limits can be computed. WANDERER and DELIMITER have been implemented in the MACSYMA system, a symbolic and algebraic manipulation system being developed at Project MAC, MIT. A typical problem in applied mathematics, namely asymptotic analysis of a definite Integral, is solved using MACSYMA to demonstrate the usefulness of such a system and the facilities provided by WANDERER.