Answer
Shown
Work Step by Step
By substitution $u=1-x\,\,\,du=-dx$, we have
$\int_{0}^{1}x^a(1-x)^b\,dx=-\int_{1}^{0}(1-u)^au^b\, du=\int_{0}^{1}u^b(1-u)^a\, du$
Now, since the result of the integrals does not depend on the $x$ or $u$ (they are actually the same instead we wrote $u$ is just make it more readable), therefore we have shown what the question asked.
