Consider points $\mathrm{P}$ and $\mathrm{Q}$ in the $x\text{-}y$ plane, with $P=(1,0)$ and $Q=(0,1)$. The line integral $\displaystyle{}2 \int_{P}^{Q}(x d x+y d y)$ along the semicircle with the line segment $P Q$ as its diameter
- is $-1$
- is $0$
- is $1$
- depends on the direction (clockwise or anti-clockwise) of the semicircle