Answer
$\dfrac{-39}{2}$
Work Step by Step
Since, we have $\int_C F \cdot T ds-\int_C F. dr$
Now,
$\int_C F \cdot T ds-\int_C F. dr=\int_{4}^1 x^2 dx-\int_{2}^{-1} y dy$
$=[\dfrac{x^3}{3}]_{4}^1-[\dfrac{y^2}{2}_{2}^{-1}$
or, $\int_C (x-y) dx +(x+y) dy=\dfrac{-38}{2}-\dfrac{1}{2}=\dfrac{-39}{2}$
