Just a thought, we want this area (red + blue):
Red area should be easy to integrate as a simple definite integral
Thinking about the function transformations, the blue area is just this area on the original function f(x):
By differentiating to find the turning points, we find that the leftmost turning point occurs at
.
subbing this into f(x) to get the y value, say y=a, you can find the blue area as
OH DANGIT YOU STILL GOTTA FIND THE UPPER BOUND UGH thought I was cooking but this is also complicated cause you gotta find the solutions to f(x)=a
surely theres a really straightforward solution im completely missing