Hello, I don't understand how to derive the distribution of T=X+Y where each X and Y follow a uniform distribution on (0,1), precisely I do not understand how to derive the answer when 1

Secondly, can you help derive this mgf and precise for which values of s_1 and s_2 it is finite.

f_U,V (u, v) = exp((2)*u) if u > 0 and u < v < u

0 otherwise

Thank you so much