the sum of two indep U(0,1) is a triangular density
that's 0 when S=X+Y is less than 0 or greater than 2.
It's s on 0<s<1 and it's 2-s on 1<s<2.
The way to figure that out is via the CDF.
Then draw the unit square of x and y between (0,1) for both
and find this area WITHOUT integrating, use geometry.