how do I verify Green Theorem using mathematic

Verify Green’s Theorem by using Mathematica to evaluate both the line integral and the double integral of the vector field 𝑭(π‘₯, 𝑦) = 𝑦2𝑒π‘₯ π’Š + π‘₯2𝑒𝑦 𝒋 over the curve C consisting of the line segment from (-1,1) to (1,1) followed by the arc of the parabola 𝑦 = 2 βˆ’ π‘₯2 from (1,1) to (-1,1).