Integral using gamma function $\int_0^1 x^a(1-x)^b dx = \frac{\Gamma(1 + a) \Gamma(1 + b)}{\Gamma(2 + a + b)} $
Prove that $\int_0^1t^{p-1}(1-t)^{q-1}\,dt=\frac{\Gamma(p)\Gamma(q)}{\Gamma(p+q)}$ for positive $p$ and $q$