Problem $1.$ Let $F=($:$P,Q$:$)be$ a differentiable vector field defined $on$ the domain

formed $by$ the rectangle $R,$ except $at$ the centers $of$ the circles $C_2,C_3$ and $C_4$ given $in$

the picture $(with$ their corresponding orientation$).We$ know the following information:

$(1){\displaystyle \underset{C_2}{\overset{\phantom{}}{}}}Fdr=$

$(2){\displaystyle \underset{C_3}{\overset{\phantom{}}{}}}Fdr=$

$(3){\displaystyle \underset{C_4}{\overset{\phantom{}}{}}}Fdr=-$

$(4)P_y-Q_x-=-2,on$ the points $in$ which the vector field $is$ defined.

Compute

${\displaystyle \underset{C_1}{\overset{\phantom{}}{}}}Fdr$