VC4.5

Here the curve C is $y=\sqrt{1-x^2}\,$ or $x^2+y^2=1\,$ which lies on xy-plane.Again,in xy-plane, $r=xi+yj,dr=dxi+dyj\,$

Therefore $\int_{C} F\cdot\,dr=\int_{C} (\cos y i-x\sin y j)\cdot(dxi+dyj)=\int_{1,0}^{0,1} (\cos y dx-x\sin y dy)=[x\cos y]_{1,0}^{0,1}=0-1=-1\,$