# Functional Integration

Calculus Level 5

$f(x)+f \left(1-\dfrac{1}{x}\right)=\tan^{-1} x, \quad \forall x \in \mathbb{R} - \{0\}$

If $$f:\mathbb{R} \rightarrow \mathbb{R}$$ satisfies the functional equation above then $$\displaystyle\int_{0}^{1} f(x) \, dx=\frac{a \pi ^{b}}{c}$$, where $$a,b,c$$ are positive integers with $$a,c$$ coprime.

Find the value of $$a+b+c$$.

×