I've used Stokes's theorem to show that for $\displaystyle \bold{F}(\bold{x})$ a vector field,

$\displaystyle \oint_C d\bold{x} \times \bold{F} = \int_S (d\bold{S} \times \nabla) \times \bold{F} $

where the curve C bounds the open surface S.

I'm then asked to "Verify this result when C is the unit square in the xy plane with opposite vertices at

(0,0,0) and (1,1,0) and $\displaystyle \bold{F}(\bold{x}) = \bold{x} $".

I do not know how to go about evaluating either of these integrals. Any advice would be appreciated.

Thanks