Let a Denote the Area Enclosed by the Graph $( x ) = \frac { 1 } { x + 1 }$

Multiple Choice

Let A denote the area enclosed by the graph $( x ) = \frac { 1 } { x + 1 }$ , the x-axis, and the lines x = 1 and x = 5. Graphing the region and using plane geometry, we can find that A is

A) $\lim _ { n \rightarrow \infty } \sum _ { k = 0 } ^ { n } \left( \frac { 1 } { \frac { 4 k } { n } + 1 } \right) \left( \frac { 4 } { n } \right)$
B) $\lim _ { n \rightarrow \infty } \sum _ { k = 0 } ^ { n - 1 } \left( \frac { 1 } { \frac { 4 k } { n } + 1 } \right) \left( \frac { 4 } { n } \right)$
C) $\lim _ { n \rightarrow \infty } \sum _ { k = 1 } ^ { n } \left( \frac { 1 } { \frac { 5 k } { n } + 1 } \right) \left( \frac { 5 } { n } \right)$
D) $\lim _ { n \rightarrow \infty } \sum _ { k = 0 } ^ { n - 1 } \left( \frac { 1 } { 4 k } + 2 \right) \left( \frac { 4 } { n } \right)$
E) $\lim _ { n \rightarrow \infty } \sum _ { k = 0 } ^ { n - 1 } \left( \frac { 1 } { \frac { 5 k } { n } + 1 } \right) \left( \frac { 4 } { n } \right)$