I will assume you mean "rotate the region bounded by the graphs of $f$ and $g$ about the line $y=c$".
Using the shell method, you would revolve a horizontal line segment bounded by the graphs of $f$ and $g$ about $y=c$ to generate a shell.
Let's assume the left endpoint of the line segment at height $y$ is always given by $f^{-1}(y)$ and the right endpoint is always given by $g^{-1}(y)$. Also assume the region bounded by the graphs of $f$ and $G$ lies below the line $y=c$. And finally assume that the graphs of $f$ and $g$ have exactly two points of intersection: "the bottom" at $y=a$, and "the top" at $y=b$
The horizontal line segments would then range from $y=a$ to $y=b$.
The width of the horizontal line segment at height $y$ would be $g^{-1}(y)-f^{-1}(y)$.
Finally, the distance from the line segment at height $y$ to the line $y=c$ would be $c-y$.
The shell method would then give the integral $2\pi\int_a^b \bigl( g^{-1}(y)-f^{-1}(y)\bigr)(c-y)\,dy.$