1.7 Let $f$ and $g$ be continuous functions of both variables on $[0, 1] \times [0, 1]$. Show that \\
$\int_0^x g(x, s) ds \int_s^1 f(s, t) dt = \int_0^1 \{\int_0^{\min(x, t)} g(x, s) f(s, t) ds\} dt$, \\
$\int_x^1 g(x, s) ds \int_0^s f(s, t) ds = \int_0^1 \{\int_{\max(x, t)}^1 g(x, s) f(s, t) ds\} dt$. \\
(Diagrams like Figure 1.1 may help in carrying out the necessary changes in integration orders. The results given are true under less stringent conditions on $f$ and $g$.)
