The range of symbols available depends on the fonts used, and the classic Computer Modern collection doesn't have a bold version of the symbol extension font used for integral signs.
Assuming you don't want to change font setup globally there are a couple of choices. Use an extra set of
\bm sees this as a complex expression and just uses
\boldmath internally. This will make the other symbols bold but leave the integral sign from the standard font. or you could modify the poor man's bold to offset the symbols by a smaller amount so the gaps don't show. The original used an arbitrary value of
.4mu here I use