Find density functions from two dimensional function

Find density functions from two dimensional function

I am given a density function of a two-dimensional vector and have to find
the density functions for both X and Y.
The functions can be seen here,
http://i.imgur.com/KlsThlf.png
I know I have to integrate the two-dimensional function with respect to X
and Y, but I am having trouble understanding which limits I should use,
and why.
It is fairly obvious that the limits for $f_Y(y)$ is $0$ and $5y$, as that
is the interval for $x$ in the given function, so therefore,
$$f_Y(y)=\int_0^{5y}\frac{2}{5}dx=2y$$
But what about $f_X(y)$? I would think that the limits would be $0$ and
$1$, as that is the interval for $y$. But the following,
$$f_X(x)=\int_0^{1}\frac{2}{5}dy=0.4$$
Is just plain wrong. Please help me understand the limits for these
density functions. I have no idea what is going on :)
Thanks.