Can anyone provide a (non-geometrical) proof of the following change of variable trick? $ \int_a^b\int_a^t f(s)g(t)\,ds\,dt=\int_a^b\int_s^b f(s)g(t)\,dt\,ds$
For $f$ and $g$ complex-valued functions of the real variable sufficiently integrable for these expressions to make sense.