JEE Advance - Mathematics (1992 - No. 17)

A cubic $$f(x)$$ vanishes at $$x=2$$ and has relative minimum / maximum at $$x=-1$$ and $$x = {1 \over 3}$$ if $$\int\limits_{ - 1}^1 {f\,\,dx = {{14} \over 3}} $$, find the cubic $$f(x)$$.