I'd love your help with proving that:
For continuous function $f$, $\int_{0}^{x} \left[\int_{0}^{t}f(u) \; du \right] \; dt = \int_{0}^{x} f(u)(x-u)du$
I'm not quite sure what I should do with this.
From Newton-Leibniz theorem I get that the left side of the equation is $(F(t)-F(0))x$, while on the right side I wanted to do an integration by parts, but I'm not sure how or if it is the direction.
Thanks a lot for the help.