#### Answer

$\dfrac{25}{6}$

#### Work Step by Step

Given: $\int_C F \cdot T ds-\int_C F. dr=\int_C xy dx +(y-x) dy$
Now,
$\int_C xy dx +(y-x) dy=\int_C x(2x-1) dx + \int_C (2x-1-x) (2 )dx$
or, $\int_{1}^{2} 2x^2 +x-2 dx=[\dfrac{2x^3}{3}+\dfrac{x^2}{2}-2x]_1^2$
Thus, $(\dfrac{16}{3})+2-4-(\dfrac{2}{3}) -(\dfrac{1}{2})-2=\dfrac{25}{6}$