I recently wrote "giving in to temptation" in an English assignment. My teacher told me that this was incorrect, and that it should have been "giving into temptation." This doesn't seem to make sense. Which version is correct?
The teacher is wrong. The phrasal verb is 'to give in'. You can see this by consulting any dictionary, e.g.
to finally agree to something that someone wants after first refusing: If you want them to give in you'll have to offer them more than that.
› to accept that you have been defeated and stop arguing or fighting: After months of resisting the takeover, the company was forced by its shareholders to give in.
As you can see from those dictionary examples, the word 'to' does not inevitably follow the verb.
It happens that there is a (British) verb 'to give into' but it is unusual and has a completely different meaning. It would certainly not be used with respect to temptation.
To give in to something is obviously correct. It means to no longer keep yourself from doing something you want to do (like temptation, yes.)
Here's a nice link: http://www.oxforddictionaries.com/definition/english/give
Cease fighting or arguing; admit defeat: he reluctantly gave in to the pressure
You are correct. "In" is part of the verb phrase "giving in", not part of the preposition. "Into" describes motion or transformation from one place or state to another; giving isn't that sort of action.
I'm not sure how well respected this source is, but it describes succinctly the case where "in" is part of the verb.
The correct version is
giving in to temptation
"Giving in" is a phrasal verb, i.e., a verb plus another word, usually a preposition, that has a meaning as a unit. Here, the verb means "to surrender" and it takes a prepositional phrase with "to" and the object indicating the winning party, in the example metaphorically the bad desire.
Into is a preposition that indicates contact (e.g., crashing into a car) or entry in various senses (e.g, walking into a house). Neither of those meanings makes sense in the example.