To find the marginal PDFs here is what I did so far:

Marginal Distribution of x:

f(x) = integral from 0 to 1, e^(-x)dy = ye^(-x)

after evaluating I got e^(-x)

Marginal Distribution of y:

f(y) = integral from 0 to inf, e^(-x) = -e^(-x)

after evaluating I got 1

Am I evaluating each one using the wrong boundaries?