## Riemann Summ Limit Proof (strange question to me)

Recall the definition of teh Riemann Sum $S(f;\pi ;\xi)$ for a function $f:[0,1]\rightarrow \mathbb{R}$.
Let $f:[0,1]\rightarrow \mathbb{R},\ x\rightarrow \frac{5}{6}x$[/latex] For the partition $\pi_n$ of $[0,1], 0=t_0 and $\xi_j =\ \frac{2}{3}t_j\ +\ \frac{1}{3}t_(j+1)\in [t_j,t_(j+1)]$ find $S(f;\pi_n,\xi)$.

Now Prove $lim(n\rightarrow infinity)\ of\ S(f;\pi_n,\xi)=\frac{5}{12}$

Pretty clueless on this question. A walk through on the steps would be nice for the test coming.