I was wondering if someone could possibly tell me what this integral is or possibly help me figure out an upper and lower bound for this integral (in terms of $X,Y,\alpha$):
$\int_{X}^{Y} v^{\alpha} (1-v)^{\alpha} dv$, where $-1< \alpha <0$ and $0< X < Y <1$. $\alpha, X, Y$ are all real numbers.
Thank you!