Green's theorem

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${\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)}$
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In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D (surface in ${\displaystyle \mathbb {R} ^{2}}$) bounded by C. It is the two-dimensional special case of Stokes' theorem (surface in ${\displaystyle \mathbb {R} ^{3}}$). In one dimension, it is equivalent to the fundamental theorem of calculus. In three dimensions, it is equivalent to the divergence theorem.