Use the Limit Process to Find the Area of the Region

Multiple Choice

Use the limit process to find the area of the region between $f ( x ) = \frac { 1 } { 4 } \left( x ^ { 2 } + 4 x \right)$ and the $x$ -axis on the interval $[ 1,4 ]$ .

A) $\frac { 143 } { 2 }$
B) $\frac { 81 } { 4 }$
C) $\frac { 47 } { 2 }$
D) 78
E) $\frac { 51 } { 4 }$