In reply to Phonetic symbols in Calibri and Cambria:
The integral sign has more freedom in its shape since it doesn't have the constraints of the phonetic esh symbol. The latter has to work as a phonetic symbol alongside the lowercase latin letters and similar symbols that make up the various phonetic alphabets, and in addition it can have diacritics.
Many of the diacritics used in the IPA go below the letter they modify. If the letter has a descender, the same diacritic is used above the letter. So the 'ring below' diacritic for devoicing normally goes below the letter as in 'd̥', but it goes above the letter as in 'ɡ̊'. But the esh symbol has both a descender and an ascender, so it's tricky what to do with such diacritics (the 'ring below' wouldn't make sense since the esh stands for a sound which is already voiceless, but we could combine it with a 'caron below' for voicing). One solution I've seen puts the diacritic as a sort of a spacing modifier after the esh symbol, not under it. The trouble is that some of these diacritics are only encoded as combining diacritics in Unicode and not as spacing modifiers, so you have to cheat by combining the diacritic with a space.