Sketch the integrand!

Calculus Level 2

2πππ/23π/2(((xπ)2)1/4sin(x)+π2)dx\frac{\sqrt{2}}{\pi\sqrt{\pi}}\int_{\pi/2}^{3\pi/2}\left(((x-\pi)^2)^{1/4}\sin(x)+\sqrt{\frac{\pi}{2}}\right) \, dx

Without using a calculator, evaluate the integral above.

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