I've heard these called the German or Russian style integral sign. I don't know the actual history. I have seen this question [1] on the tex/latex stackexchange about making this integral sign.

I would expect a journal to not use a different font integral sign, however. Or rather, I would expect the "house style" to include font choices for integral signs as well. I'm not aware of any journal that uses this type of integral now, but I suppose I should also note that I mostly read papers from the arxiv now anyway.

[1]: https://tex.stackexchange.com/questions/170028/integral-sign...