I am still not getting it (although closer). First of all, what the graph would look like in 3D? I have the 'triangle' area on XY-plane, bounded by (0,0), (0,1) and (2,0), according to the bounds of X and Y. Then I have the third dimension in the direction Z (z=x+y is a plane right?), which can take values from 0 to 3. But in between these values (of z, from 0 to 3), the function of z=x+y is not the same - ie the probability of z is not determined by one function on the interval - there will be three different density functions on the intervals from 0 to 1, 1 to 2 and 2 to 3.

on 0<z<1, I think I can take z=x+y as the 'top' curve, so the density function for 0<z<1 would be

Further on, for 1<z<2 and 2<z<3, I am still not sure how to proceed...

PS I realise this is now about competing the question, not just about intervals for z, but I guess I need help with the whole thing...