Set Up the Definite Integral That Gives the Area of the Region

Multiple Choice

Set up the definite integral that gives the area of the region bounded by the graphs. $\begin{array} { l } f ( x ) = ( x - 4 ) ^ { 3 } \\g ( x ) = x - 4\end{array}$

A) $\int _ { 3 } ^ { 4 } \left( ( x - 4 ) - ( x - 4 ) ^ { 3 } \right) d x + \int _ { 4 } ^ { 5 } \left( ( x - 4 ) ^ { 3 } - ( x - 4 ) \right) d x$
B) $\int _ { - 1 } ^ { 0 } \left( ( x - 4 ) + ( x - 4 ) ^ { 3 } \right) d x + \int _ { 0 } ^ { 1 } \left( ( x - 4 ) ^ { 3 } + ( x - 4 ) \right) d x$
C) $\int _ { - 1 } ^ { 0 } \left( ( x - 4 ) ^ { 3 } - ( x - 4 ) \right) d x + \int _ { 0 } ^ { 1 } \left( ( x - 4 ) - ( x - 4 ) ^ { 3 } \right) d x$
D) $\int _ { 3 } ^ { 4 } \left( ( x - 4 ) ^ { 3 } - ( x - 4 ) \right) d x + \int _ { 4 } ^ { 5 } \left( ( x - 4 ) - ( x - 4 ) ^ { 3 } \right) d x$
E) $\int _ { 3 } ^ { 4 } \left( ( x - 4 ) ^ { 3 } + ( x - 4 ) \right) d x + \int _ { 4 } ^ { 5 } \left( ( x - 4 ) + ( x - 4 ) ^ { 3 } \right) d x$