double integral to find the volume

Question

i have to find the integral above a triangle with vertices (0,2), (1,1) and (2,2) and under the surface z=xy. I understand the concept of using the double integral to find the volume, but my issue is to set the limits for my integral. Finding the lines passing through (0,2)->(1,1) and (2,2)->(1,1) gives me the lines y = -x+2 and y=x. My problem now is: do i use x = 2-y and x = y as the limits, or y = -x+2 and y=x. It gives a different integral. I hope my question is somehow clear. Thank you in advance!

Answer 1

Fix $y∈[1,2]$ and find the interval of variation of $x$ corresponding to that $y$, as in the following picture.