(c) That line integral around the unit circle equals

True or false, with reason:

(a) When $\mathbf{F}=y\mathbf{i}$ the line integral $\int \mathbf{F}\cdot d\mathbf{R}$ along a curve from $P$ to $Q$ equals the usual area under the curve.

(b) That line integral depends only on $P$ and $Q$, not on the curve.

(c) That line integral around the unit circle equals $\pi$.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §15.2 Line Integrals, #44