The function $f$ is one-to-one, and the shaded region between the lines $y = x$ and $x = 1$ and the curve $y = f ( x )$ in the first quadrant is given below. Which of the following is the expression of the area of the shaded region in terms of $\mathbf { f } ^ { - \mathbf { 1 } } ( \mathbf { x } )$? A) $\int _ { 0 } ^ { 2 } f ^ { - 1 } ( x ) d x$ B) $\int _ { 0 } ^ { 2 } \left( 2 - f ^ { - 1 } ( x ) \right) d x$ C) $\int _ { 0 } ^ { 1 } \left( x - f ^ { - 1 } ( x ) \right) d x$ D) $\int _ { 0 } ^ { 1 } \left( 2 - f ^ { - 1 } ( x ) \right) d x + \int _ { 1 } ^ { 2 } f ^ { - 1 } ( x ) d x$ E) $\int _ { 0 } ^ { 1 } \left( x - f ^ { - 1 } ( x ) \right) d x + \int _ { 1 } ^ { 2 } \left( 1 - f ^ { - 1 } ( x ) \right) d x$
The function $f$ is one-to-one, and the shaded region between the lines $y = x$ and $x = 1$ and the curve $y = f ( x )$ in the first quadrant is given below.
Which of the following is the expression of the area of the shaded region in terms of $\mathbf { f } ^ { - \mathbf { 1 } } ( \mathbf { x } )$?\\
A) $\int _ { 0 } ^ { 2 } f ^ { - 1 } ( x ) d x$\\
B) $\int _ { 0 } ^ { 2 } \left( 2 - f ^ { - 1 } ( x ) \right) d x$\\
C) $\int _ { 0 } ^ { 1 } \left( x - f ^ { - 1 } ( x ) \right) d x$\\
D) $\int _ { 0 } ^ { 1 } \left( 2 - f ^ { - 1 } ( x ) \right) d x + \int _ { 1 } ^ { 2 } f ^ { - 1 } ( x ) d x$\\
E) $\int _ { 0 } ^ { 1 } \left( x - f ^ { - 1 } ( x ) \right) d x + \int _ { 1 } ^ { 2 } \left( 1 - f ^ { - 1 } ( x ) \right) d x$