Write the Limit $[ 0,8 ]$ Where $c _ { i }$

Multiple Choice

Write the limit $\lim _ { | \Delta x | \rightarrow 0 } \sum _ { i = 1 } ^ { n } 4 c _ { i } \left( 7 - c _ { i } \right) ^ { 2 } \Delta x _ { i } , \text { as a definite integral on the interval }$ $[ 0,8 ]$ where $c _ { i }$ is any point in the $i ^ { t h }$ subinterval.

A) $\int 4 x(7-x) ^{8} d x$
B) $\int_{8}^{0} 4 x^{2}(7-x) ^{8} d x$
C) $\int 4 c_{i}\left(7-c_{i}\right) ^{2} \Delta x_{i}$
D) $\int_{0}^{8} 4 x(7-x) ^{2} d x$
E) $\int_{0}^{c_{i}} 4 c_{i}\left(7-c_{i}\right) ^{2} \Delta x_{i}$