Difficult definite integral with a possibly real finite answer

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The Integral

I'm stumped here.The interval of integration would make me think to look for symmetry, but it's clearly not even or odd. I asked wolfram alpha to get any ideas, and it gave me a complex number as the value of the integral, which makes no sense. The graph seems to enclose a finite area in the interval, making me think it has a real finite answer. How do I solve this?