How can I find the area between the graphs of a function and its inverse? I have the following function $$f(x)=x\cdot e^{x^2-1} $$ and I want to find the are between this function and its inverse. I'm not sure how to calculate the integral because I know that for this type of problem I need to find where the two functions intersect.

HINT: The functions intersect where $f(x)=x$.
HINT2: This is at $-1, 0, 1$
HINT3: The inverse function is the function reflected around the line $y=x$, so you find the intersections of $f(x)$ and $f^{-1}(x)$ when $f(x)$ intersects with $y=x$. You use this to integrate and find the area between $f(x)$ and $x$, then multiply by $2$ for symmetry.
