If f(x)+2f(1-x)=x^2+1 ∀ x ∈ R then f(x) is

$f(x) + 2f(1 − x) = x^2 + 1$

Replacing x → (1 − x) we get

$f(1 − x)+2f(x)=(1-x)^2+1$ 

$⇒f(1 − x)+2f(x)=2+x^2-2x$

 From these equations we get $f(x)=\frac{1}{3}(x^2-4x+3)$