# Interesting Integrals 10

Calculus Level 4

$\large\int_{0}^{\sin^2 (x)}{\sin^{-1} \left( \sqrt t \right)}\,dt\ + \large\int_{0}^{\cos^2 (x)}{\cos^{-1} \left( \sqrt t \right)}\,dt=\dfrac{\pi}{c}$

The equation above holds true for some positive integer $$c$$. Find $$c$$.

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