3.4: Shaded area with $y=6+e^{4x-5}$ and $x=2$

The diagram shows part of the graphs of $y=6+e^{4x-5}$ and $x=2$. The line $x=2$ meets the curve at $B(2, b)$ and the line $AB$ is parallel to the $x$-axis. Find the area of the shaded region.