If you integrate with respect to \( dx \) first, the corresponding inner integral limit should be \( \int_{-\infty}^y \).

i.e. \( \int_{-\infty}^{+\infty} \int_x^{+\infty} f(x, y) dydx = \int_{-\infty}^{+\infty} \int_{-\infty}^y f(x, y) dxdy \)

Changing the integration order will also change the limits.

Also I am not sure if you can directly claim \( I_{1,1} = 0 \)