CDF of Sum of Random Variables

CDF of $Z$ is is: $F_Z(z)=P(Z\le z)=P(X+Y\le z)$

$$\{\begin{array}{l}\int {\int }_R{f}_{X,Y}(x,y)dxdy\\ \sum {\sum }_R{p}_{X,Y}(x,y)\end{array}$$