Question 1 Let $f: [0, c] \rightarrow \mathbb{R}$ be continuous.
(a) Sketch the region we integrate over in $\int_0^c \int_0^x f(y) \, dy \, dx$.
(b) Use part (a) to change the order of integration and prove that
$\int_0^c \int_0^x f(y) \, dy \, dx = \int_0^c (c - y)f(y) \, dy$.