Normally, you would just integrate the joint density over all possible values of Y:
[tex]f_X(x) = \displaystyle \int_{-\infty}^\infty f_{X,Y}(x,y) \, dy[/tex]
However, the given joint density is not actually a valid density function, since
[tex]\displaystyle \int_{-\infty}^\infty f_{X,Y}(x,y) \, dx\, dy = \int_0^2 \int_0^1 (x+y) \, dx \, dy = 3 \neq 1[/tex]
so the question is not well-posed.
