finding the area using integral 
Find the area blocked between X-Y axis and $x=\pi$, $y=\sin x$ according to $x$ and $y$.

According to x: $\int_0^\pi \sin x \, dx=-\cos(\pi)+\cos(0)=2$
According to $y$: $\int_0^1 (\pi- \sin^{-1} y)\,dy=\left[\pi y-\sin^{-1}y + \sqrt{1-y^2}\right]_0^1 = \pi-\frac{2}{\pi}+1=\frac{2}{\pi}+1$
Where did I get it wrong?

I don't get the second approach, since $\sin (x)=\sin (\pi-x)$ Would it be $2\int _0^1 \left(\frac{\pi}{2}-\sin ^{-1}y\right)dy=\left(-\sqrt{1-y^2}+\frac{\pi  y}{2}+y \left(-\sin ^{-1}(y)\right)\right)\left.\right|_0^1=2$? Hope it will help
