problem on line integral using stoke's theorem

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enter image description here In these line if we use Stoke's theorem in plane won't it be zero on converting it to double integral as the partial derivative of coefficient of y w.r.t x minus that of x w.r.t y is 0 . but its answer is given to be 1 . if my approach is wrong why can't we use stoke's theorem here? What alternate approach can be used?