You misunderstood. Your professor said your solutions broke Calculus. Congratulations on violating the laws of mathematics and still getting the correct answer .
The highschool teacher responsible for teaching me trig identities and log/e^x was going through a breakup with her girlfriend or some shit during those weeks. So instead of learning those things we did cross word puzzles and word finds.
Needless to say, integration was... difficult to learn. Because I got to give myself remedial math lessons at the same time, in the era before Kahn academy and helpful Indian YouTube videos.