IMO 1992 Problem 2

Let $\,{\mathbb{R}}\,$ denote the set of all real numbers. Find all functions $f: {\mathbb{R}}\rightarrow {\mathbb{R}}\,$ such that $$f\left( x^{2}+f(y)\right) =y+\left( f(x)\right) ^{2}\hspace{0.2in}\text{for all} x,y\in \mathbb{R}.$$