Love's equation $f(x)+\frac{1}{\pi} \int_{-1}^{1} \frac{f(t)}{1+(x-t)^2}dt=1, \ \ (|x|\geq 1)$

Question

Let us consider Love's equation: $$f(x)+\frac{1}{\pi} \int_{-1}^{1} \frac{f(t)}{1+(x-t)^2}dt=1, \ \ (|x|\geq 1)$$ Is $f(x)$ a two times differentiable function?