9.4.13 Curvilinear integrals

Problem: Calculate the line integral of the 2nd kind. \[ \int_{\Gamma} y d x-\left(y+x^{2}\right) d y \] where \( \Gamma \) is the arc of the parabola \( y=2 x-x^{2} \) from point \( A(2 ; 0) \) to point \( B=(0 ; 0) \).