By considering $\displaystyle \overset{1}{\underset{0}{\int}}xB_{n}(x)\, dx$.

I am trying to prove that

$\displaystyle B_{n+1}=(n+1)\overset{n}{\underset{r=0}{\sum}}\lef t(\begin{array}{c}

n\\

r\end{array}\right)\frac{B_{r}}{n-r+2}$

but failing miserably, despite trying to integrate by parts.

Any takers?