10.1.4 Integral of a complex variable

Problem: Calculate the integral of the function of the complex variable \( f(z)=u(x, y)+i v(x, y) \) along the given arc \( \widetilde{A B} \) : \[ \begin{array}{l} f(z)=(2 x y-x-y+1)+i(3 x y+2 x+2 y+1), \\ \widetilde{A B}: y=x^{2}-2 x-3, A(-4 ; 5), B(0 ;-3) . \end{array} \]