
double integrals
given that vector filed F= < 2x+ sin y, xcosy>, find integral F.dr where C is the arc y=1x^2 from (0,1) to (1,0).
my working
integral F. dr = double integral curl F dxdy =0.
what is wrong with my workings?
i know that i can make use of F= grad f to solve this question..but im just wondering why my this method doesnt give me the correct answer.

To use Stock teorem curve must be closed and make a boundary to surface integral, in your case it is not.

i understand that to be a closed curve, it means to be something like a circle, where the curve starts and ends at the same point.
but what does it mean that it makes a boundary to surface integral?
thanks!