Recall the definition of teh Riemann Sum $\displaystyle S(f;\pi ;\xi)$ for a function $\displaystyle f:[0,1]\rightarrow \mathbb{R}$.
Let $\displaystyle f:[0,1]\rightarrow \mathbb{R},\ x\rightarrow \frac{5}{6}x$[/latex] For the partition $\displaystyle \pi_n$ of $\displaystyle [0,1], 0=t_0<t_1<...<t_n,\ t_j\ =\ \frac{5}{n},\ j=0,...,n$ and $\displaystyle \xi_j =\ \frac{2}{3}t_j\ +\ \frac{1}{3}t_(j+1)\in [t_j,t_(j+1)]$ find $\displaystyle S(f;\pi_n,\xi)$.

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

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