Is this notation ambiguous?

Question

Is this notation for evaluation of integral ambiguous? $$\int_R f(x)\,dx=F(x)\Big\lvert_{\partial R}$$ Where $R$ is the domain of integration and $\partial R$ its boundary. I'd like to include it in a simple proof that I have to do.

EDIT:

The domains that I have to deal with in the proof are either closed intervals or $(-\infty,\infty)$. And the integration above is just the fundamental theorem of calculus.

Answer 1

I don't think it's ambiguous at all. I would say to clarify it exactly as you did whenever using it.

Answer 2

I see no ambiguity.

It is pretty much Stokes' theorem, which is also written as $$\int_\Omega d\omega = \oint_{\partial\Omega} \omega$$ with $\omega=F(x)$ in your case.

I think that at worst it will just be unfamiliar to people, but not ambiguous.