Let a Denote the Area Enclosed by the Graph $f ( x ) = ( x - 1 ) ^ { 2 },$

Multiple Choice

Let A denote the area enclosed by the graph $f ( x ) = ( x - 1 ) ^ { 2 },$ the x-axis, and the lines x = 2 and x = 9. Graphing the region and using plane geometry, we can find that A is

A)
$\lim _ { n \rightarrow \infty } \sum _ { k = 1 } ^ { n } \left( \frac { 7 k } { n } - 1 \right) ^ { 2 } \left( \frac { 7 } { n } \right)$
B) $\lim _ { n \rightarrow \infty } \sum _ { k = 1 } ^ { n } \left( \frac { 7 k } { n } + 1 \right) ^ { 2 } \left( \frac { 7 } { n } \right)$
C) $\lim _ { n \rightarrow \infty } \sum _ { k = 1 } ^ { n } \left( \frac { 7 k } { n } + 2 \right) ^ { 2 } \left( \frac { 7 } { n } \right)$
D) $\lim _ { n \rightarrow \infty } \sum _ { k = 1 } ^ { n } \left( \frac { 9 k } { n } + 2 \right) ^ { 2 } \left( \frac { 9 } { n } \right)$
E) $\lim _ { n \rightarrow \infty } \sum _ { k = 1 } ^ { n } \left( \frac { 9 k } { n } + 1 \right) ^ { 2 } \left( \frac { 9 } { n } \right)$