Solve this integral for free WiFi I saw this today, I checked in Mathematica and the integral comes out to $\pi$, but I have no idea how to solve it.

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  $$\int_{-2}^2\left(x^3\cos\frac x2+\frac12\right)\sqrt{4-x^2}\ dx$$



The integrand is the sum of an odd and even function, and only the latter contributes, so it's $\int_0^2\sqrt{4-x^2}dx$. This is a quarter of the area of a radius-$2$ circle, i.e. $\pi$.
