Investigate the existence and, if possible, determine the value of the integrals below:
$\int_{[0,1]^2}f(x,y) d(x,y)$, $\int_0^1 \int_0^1 f(x,y) dx dy$, $\int_0^1 \int_0^1 f(x,y) dy dx$
where $f(x,y) = \frac{x^2 - \frac{1}{3}}{y^2}$.
If computed the second integral: $\int_0^1 \int_0^1 f(x,y) dx dy$, which is $0$, and the third: $\int_0^1 \int_0^1 f(x,y) dy dx$ which is $\infty$, if I'm correct. But I dont know how to calculate the first one. Could somebody help me please?