I.12.12 Vector field circulation

Condition: Calculate the circulation of the vector field \( \vec{a}=P(x, y) \vec{\imath}+Q(x, y) \vec{\jmath} \quad \) along the closed contour \( L \) lying in the plane \( X O Y \) (traversal counterclockwise). \( \vec{a}=2 \vec{\imath}-(y+1) \vec{\jmath}, \quad L: \quad \) parallelogram \( \quad \) with vertices at points \( A(2,0), B(0,2), C(-5,2) \), \( D(-3,0) \)