The function $f ( x )$ is increasing and $f ( 0 ) = 0$.
The positive constants $a$ and $b$ are such that $a < b$.
The area of the region enclosed by the curve $y = f ( x )$, the $x$-axis and the lines $x = a$ and $x = b$ is denoted by $R$.
The function $g ( x )$ is defined by $g ( x ) = f ( x ) + 2 f ( b )$.
Which of the following is an expression for the area enclosed by the curve $y = g ( x )$, the $x$-axis and the lines $x = a$ and $x = b$ ?
A $\quad R + ( b - a ) f ( b )$
B $R + 2 ( b - a ) f ( b )$
C $\quad R + 2 f ( b ) - f ( a )$
D $R + 2 f ( b )$
E $\quad R + ( f ( b ) ) ^ { 2 }$
F $\quad R + ( f ( b ) ) ^ { 2 } - ( f ( a ) ) ^ { 2 }$
G $\quad R + 2 ( f ( b ) - f ( a ) ) f ( b )$