Given a function $\displaystyle f$ of a real variable which satisfies the function defined by $\displaystyle f (x) + x \times f(1-x) = 1 +x^2 $, for all real $\displaystyle x$, determine $\displaystyle f(x)$.

Please explain to me what to do. Ive never done calculus before and this is the question I was given.