2
Let $D = \{(x, y) \mid x + y \le \pi, 0 \le x, 0 \le y\}$ and
$f(s,t) = \iint_D \left[t\sin(x - y + s) + (x + y + t)^2\right] dxdy$.
(1) Calculate the double integral and find $f(s,t)$.
(2) Find all the local maxima and local minima of the function $f(s,t)$ on
the domain $E = \{(s,t) \mid 0 < s < 2\pi, t \in \mathbb{R}\}$.