If $\int_{-\infty}^\infty f(x) dx = 1$, then what is the value of $\int_{-\infty}^\infty f\left(x-\frac1{x}\right)dx$?

Question

If $$\int_{-\infty}^\infty f(x) dx = 1$$ then $$\int_{-\infty}^\infty f\left(x-\frac1{x}\right)dx$$ is equal to which of $0$, $1$, $-1$, $2$?

(original problem image)

I tried this first directly, then after putting specific functions also. In both cases, I am not getting. Can anyone please help me in this?