${\int }_P^{(1+,0+,1-,0-)}{t}^{a-1}{(1-t)}^{b-1}\mathrm{mathrm}dt=-4e^{\pi i(a+b)}\sin \left(\pi a\right)\sin \left(\pi b\right)\mathrm{mathrm}B\left(a,b\right)$