(C) We know that $\sin^{-1}(\cos x) = \sin^{-1}(\sin(\frac{\pi}{2} - x)) = \frac{\pi}{2} - x$. Therefore,the integral becomes: $\int (\frac{\pi}{2} -

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(C) We know that $\sin^{-1}(\cos x) = \sin^{-1}(\sin(\frac{\pi}{2} - x)) = \frac{\pi}{2} - x$. Therefore,the integral becomes: $\int (\frac{\pi}{2} - x) \, dx$ $= \int \frac{\pi}{2} \, dx - \int x \, dx$ $= \frac{\pi}{2}x - \frac{x^2}{2} + C$ $= \frac{\pi x - x^2}{2} + C$.