Rid is correct. This question appears to be a duplicate of Finding the next available id in MySQL
In that thread, user Eimantas provided the working solution I used. Reproduced here for convenience:
SELECT Auto_increment FROM information_schema.tables WHERE table_name='the_table_you_want';
Kudos to eggyal and GavinTowey in this thread, though, for their direction.
Future readers are advised to note Gavin's comment (to eggyal's answer) regarding race conditions (that is: another DB entry happening a split second before yours and "stealing" the ID you thought you would get).
Use of LAST_INSERT_ID() as described by eggyal is strongly recommended over the method described in this answer.
I encourage future readers to upvote eggyal's answer, as it is a better approach, but I would appreciate no further downvotes to this answer. Since this is what the question specifically asked, this is the "correct" answer - eggyals' downvotes notwithstanding. I trust there are no hard feelings; as you know, I receive no benefit for choosing my own answer as the correct one.