vector field as integral

Question

Define a vector field $ \vec{f}(\vec{R}) = \oint_C{|\vec{r} - \vec{R}|^2 d\vec{r} }$ where C is a simple closed curve.

show that there are constant vectors $ \vec{P} $ and $ \vec{Q} $ such that $ \vec{f}(\vec{R}) = \vec{R} \times \vec{P} + \vec{Q} $