Calculate the Lebesgue integral of the function
$$ f(x,y)=\left\lbrace\begin{array}{ccl}[x+y]^{2} &\quad&|x|,|y| <12 ,\quad xy \leq 0\\ 0 &\quad&\text{otherwise}\end{array} \right.$$
in $\mathbb{R}^2$.
Can anyone help with this? I can't find a way to make the expression of $f$ more simply to calculate the integral.
edit: $[\cdot]$ is the integer part.