I know that in general, you cannot break the integral up under multiplication. That is:
$\int_{a}^{b}{f(x)g(x)dx} \neq \int_{a}^{b}{f(x)dx}\int_{a}^{b}{g(x)dx}$
for most functions. Are the any functions $f(x),g(x)$ where
$\int_{a}^{b}{f(x)g(x)dx} = \int_{a}^{b}{f(x)dx}\int_{a}^{b}{g(x)dx}$
holds? I am sure this will not hold for polynomial functions (since power rule will give different degrees for the resulting classes of polynomials on both sides of the equality), but I wasn't sure if there could be a clever choice of integrable functions to make this true.