$$\begin{aligned}
& f : [ 1,3 ] \rightarrow [ 2,10 ] \\
& f ( x ) = 1 + x ^ { 2 }
\end{aligned}$$ The interval $[ 1,3 ]$ is divided into two subintervals of equal length, and the right endpoints of these subintervals are marked as $x _ { 1 }$ and $x _ { 2 }$. Then, two rectangles are drawn with each subinterval as the base and heights $f \left( x _ { 1 } \right), f \left( x _ { 2 } \right)$ respectively. If the sum of the areas of these rectangles is A and the area of the region between the function f and the x-axis is B, what is the difference A - B in square units? A) $\frac { 11 } { 2 }$ B) $\frac { 13 } { 3 }$ C) $\frac { 15 } { 4 }$ D) $\frac { 19 } { 6 }$ E) $\frac { 23 } { 6 }$
$$\begin{aligned}
& f : [ 1,3 ] \rightarrow [ 2,10 ] \\
& f ( x ) = 1 + x ^ { 2 }
\end{aligned}$$
The interval $[ 1,3 ]$ is divided into two subintervals of equal length, and the right endpoints of these subintervals are marked as $x _ { 1 }$ and $x _ { 2 }$. Then, two rectangles are drawn with each subinterval as the base and heights $f \left( x _ { 1 } \right), f \left( x _ { 2 } \right)$ respectively.
If the sum of the areas of these rectangles is A and the area of the region between the function f and the x-axis is B, what is the difference A - B in square units?\\
A) $\frac { 11 } { 2 }$\\
B) $\frac { 13 } { 3 }$\\
C) $\frac { 15 } { 4 }$\\
D) $\frac { 19 } { 6 }$\\
E) $\frac { 23 } { 6 }$