PDF of a rectangle If I want to find the $c$ of a $PDF$ when it's given:
$f_{X,Y}\left(x,y\right)=c\:\:\:\:\left(The\:area\:in\:blue\right),\:otherwise:\:0$

I try to do that:
$$\int _{\frac{1}{2}}^1\:\int _{-x+\frac{3}{2}}^1\:c\,dy\,dx+\int _0^1\:\int _{-x+\frac{1}{2}}^{-x+1}\:c\,dy\,dx=1$$
But I got $c=\frac{8}{5}$ and the result is $c=2$.
(I know we can calculate it with by calculating the area of the triangles but I am wondering to know why my way is not working)

The leftmost (rightmost) of the two blue regions is congruent to the rightmost (leftmost) of the two white regions, so exactly half the area is shaded, so $c=2$.
