What should i select as my bounds for finding E[Z]

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Given:

$\displaylines{ f(x,y) = &5xy, 0<x, y<1 \\ &0, elsewhere}$

find the expected value of: $z=\sqrt{x^2+y^2}$

do I solve using the integral:

$\int_{0}^{1}\int_{0}^{1}f(x,y)z dxdy$

or do i use: $\int_{0}^{\infty}\int_{-\infty}^{1}f(x,y)zdxdy$

Please explain how you select the bounds of the integral.