On the dog-bone contour around [-1,1], what are the arguments of these two lines approaching the real axis from above and below?

Question

I am using a dog-bone contour to integrate around the interval [-1,1]. (-1 and +1 are branch points of the integrand.)

I am using the principal branch of log, so I am restricting its argument to satisfy $-\pi < \theta \le \pi$.

So my question is: on the dog-bone contour, as the two lines approach the real axis in the limit, what are the arguments the integrand picks up?

My thinking is this: From below it picks up an argument of $-\pi$, from -1 to 0, and an argument of 0, from 0 to 1.

Then, from above, the integrand picks up an argument of $\pi$ from -1 to 0, and an argument of 0, from 0 to 1.

Is this correct?

My computations do not match a solution that I am studying, so I may be off in counting the arguments...

Thanks,