Evaluate the limit$.$

$\underset{||||0}{lim}{\displaystyle \underset{i=1}{\overset{n}{}}}(x_i^6-x_i^7)x,$ where $x_i=\frac{i}{n}$ and $x=\frac{1}{n}$

Sketch the graph of the region whose area is represented by the limit$.($Select the correct graph.$)$