The subject of this talk is the evaluation of Feynman and other integrals of mathematical physics. Such Integral calculus and hypergeometric function theory go hand in hand. A series of recent investigations that culminated in the construction of several Mathematica packages are based on Mellin–Barnes techniques, Method of Regions, hypergeometric function theory, etc., is reviewed in this talk to encourage the community to explore the use of these packages. We will provide a large number of examples which arise in many different branches of physics.The talk will be easily accessible to Bachelors, Masters and Ph.D. students, and also to other researchers who use hypergeometric functions such as in quantum chemistry and other branches of physics and mathematical physics in addition to those who work in elementary particle physics. We will also present some recent results.