I had a sort of odd question on my homework, Sin(x)^3 dx, integrated over all reals (from negative infinity to infinity). The problem also gives this morsel of ambiguity: "Hint: think before integrating. this is easy" Now my initial guess because of the antisymmetry of the function is that it equals zero. Although the problem doesn't ask for a proof of any way shape or form however, I was baffled how I would argue that I reasoned it equaled zero if I was called upon in class. So I'm wondering whether my assumption is correct as well as maybe a brief explanation. No proof needed.