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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.