[Math] Integral sign with circle (AND arrow on the circle) through it

Question

I know from multivariable calculus that the integral sign with circle in its middle means integrating along a closed path.

So when I encountered in complex analysis the above integral sign but with an arrow on the circle to indicate orientation, I automatically assumed oriented closed contour.

But now on reading my textbook carefully, it only says that the arrowed circle actually means oriented contour (and doesn't say anything about whether the contour is necessarily closed).

So what does the arrowed circle really mean? Can it really also refer to a smooth oriented arc (i.e. not a closed curve)?

Answer 1

I bet your text defines a contour as a closed curve. :)