Given a joint density $f_{XY}(x,y)$ on triangle with vertex $(5,0),(5,1),(4,1)$ I can't understand how to find integration bounds for convolution of $Z=X+Y$. I know that the solution should be $$F_z(z)=\int_{z-1}^{5}\left(\int_{z-x}^{1}f_{XY}(x,y)dy\right)dx$$
Any suggestion? :-)
Edit
Based on JeanMarie's answer is correct that if I change the vertex to $(1,0),(1,1),(2,1)$ then $$F_z(z)=\int_{1}^{z/2}\left(\int_{0}^{x}f_{XY}(x,y)dy\right)dx + \int_{z/2}^{2}\left(\int_{x}^{1}f_{XY}(x,y)dy\right)dx$$?