The value of ∫01cos-1x-x2-1-x22x-x2dx is equal to

$I \equiv \int_{0}^{1} \cos^{- 1} ((x - x^{2}) - \sqrt{(1 - x^{2}) (2 x - x^{2})}) d x$

$= \int_{0}^{1} \cos^{- 1} (x (1 - x) - (\sqrt{1 - x^{2}}) (\sqrt{1 - (1 - x)^{2}})) d x$

$= \int_{0}^{1} (\cos^{- 1} (x) + \cos^{- 1} (1 - x)) d x$

$= 2 \int_{0}^{1} \cos^{- 1} x d x$

Put $x = \cos θ$

$∴ I = 2 \int_{0}^{π / 2} θ \sin θ d θ$

$= 2 [- θ \cos θ + \sin θ]_{0}^{π / 2}$

$= 2$

The value of $\int_{0}^{1} \cos^{- 1} ((x - x^{2}) - \sqrt{(1 - x^{2}) (2 x - x^{2})}) d x$ is equal to