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 $g(x)=f(x)+2f(b)$.

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 $x=b$?