Many symbolic integration methods and algorithms have been developed to deal with definite integrals such as those of interest to physicists, theoretical chemists and engineers. These have been implemented into mathematical softwares like Maple and Mathematica to give closed forms of definite integrals. The work presented here introduces and analytically investigates an algorithm called Method of brackets. Method of brackets consists of a small number of rules to transform the evaluation of a definite integral into a problem of solving a system of linear equations. These rules are heuristic so justification is needed to make this method rigorous. Here we use contour integrals to justify the evaluation given by the algorithm.