The STIX fonts are designed such that to place the scripts next to large operators (e.g. integrals) you first use the advance width of the glyph to place the subscript. Then to place the superscript, you move to the right by adding the italic correction.
However, according to Khaled Hosny (XeTeX) who knows that from Murray Sargent (Microsoft) the placement of scripts with the MATH table is in the other way around: you first place the superscript using the advance width and then place the subscript by substracting the italic correction.
A related problem is that STIX Word does not have any italic correction table.
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