LaTeX: typically let software decide for me, override if it looks bad.
Paper: Too shit at writing to make a consistent choice
Depends on if the integral is integrated in the text or if it gets its own area
(a, b) at the bottom. It's a 1d integral, so nothing goes after f as well for me.
Best answer, although I work with delta "functions" a lot so I actually have to be careful picking which interval with boundary {a,b} to pick (for example, if I integrated δ(t-a)+δ(t-b) over all t in (a,b), I'd get 0, but if I integrated those deltas over (a,b] I'd get 1, and integrating over [a,b] would give 2).
Also I do have to do integrals with parameters and multiple variables so I can't really leave out the differential.
A fits on paper much better than B, especially when you try to write as small as possible to fit all of your work on one line
ConTeXt has some nice new features: https://www.pragma-ade.com/general/manuals/mathincontext-screen.pdf#page87
