If $\int_0^2\left(\sqrt{2 x}-\sqrt{2 x-x^2}\right) d x=\int_0^1\left(1-\sqrt{1-y^2}-\frac{y^2}{2}\right) d y+\int_1^2\left(2-\frac{y^2}{2}\right) d y+1$
Select the correct option:
A
$\int_0^1\left(1+\sqrt{1-y^2}\right) d y$
B
$\int_0^1\left(\frac{y^2}{2}-\sqrt{1-y^2}+1\right) d y$
C
$\int_0^1\left(1-\sqrt{1-y^2}\right) d y$
D
$\int_0^1\left(\frac{y^2}{2}+\sqrt{1-y^2}+1\right) d y$
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