$\displaystyle f(x,y) = \left\{ \begin{array}{rcl}

1 & \mbox{for} & 0 \leq x \leq 1, \ \ 0 \leq y \leq 1\\

0 & \mbox{for} & \mbox{otherwise}

\end{array}\right.$

What is $\displaystyle P \left( x-y > \frac{1}{2} \right)$

would the solution be $\displaystyle \int^{0.5}_{0} \int^{0.5-y}_0 1 dxdy = \ \ \int^{0.5}_{0} x \ \bigg{|} ^{0.5-y}_{0} dy = \ \ \int^{0.5}_{0} 0.5-y \ dy = \ \ 0.25y -\frac{y^2}{2} \ \bigg{|}^{0.5}_{0}$ ?