In his memoir-like short story book, "Surely You're Joking, Mr. Feynman!”,  Nobel-winning physicist Richard Feynman taunted an integration trick his high school physics teacher Mr. Bader taught him. According to Mr. Feynman, he used this trick to compute certain definite integrals that "guys at MIT or Princeton had trouble doing", and thus earned a great reputation for doing obscurely hard integrals, which often appear in Quantum Field Theory. In this short excursion, we will study this trick, then put it into action to evaluate the Gaussian integral, which is arguably the most useful definite integral in Probability and Data Science. Lastly we will solve one of the most difficult integral question in the 2005 Putnam competition.