I have noticed that there is a suggestion to make integral and integration synonymous in the list of suggested synonyms. See also synonyms for integration. (The users with sufficient rep in that tag can vote there.)
I believe that it is useful to have some discussion before making changes to tags containing large number of questions. In this way we will find out whether MSE users approve joining these two tags together and, if they are going to be kept separate, perhaps the usage of these two tags could be clarified a little more. (This might lead to improvement of the tag-wikis, if we find out that it is needed.)
My understanding of the two tags is that the integral tag should be used solely for questions dealing with computation of integrals, whether integration includes anything related to integration - theorems, definitions, proofs, etc. At least this is how I read the tag-excerpts for these two tags. I also had some discussion about these tags in chat and this older questions is also related: Tags derivatives, integral, limit only for computation questions?
Questions on the evaluation of definite and indefinite integrals
All aspects of integration, including the definition of the integral and computing indefinite integrals (antiderivatives).
So these are the main questions, for which I would like to know the opinion of other users:
EDIT: I'd say the situation here is similar to derivatives and differentiation, which is already an approved synonym. The tag-excerpt for derivatives does not say that it is for computation of derivatives only. (IIRC there used to be something along those lines in the tag-excerpt some time ago.) Now the tag-excerpt says: "Questions on the evaluation of derivatives or problems involving derivatives (for example, use of the mean value theorem)."
EDIT 2: Now I have found the suggestion to make them synonyms in the long thread on tag merging and synonyms. This suggestion has 6 upvotes and no downvotes there. (As you can see, I have commented there, but I somehow managed to forget that this was discussed in that thread.)