I picked up these books while trudging through some dungeons and I can't get rid of them because the game says they are quest items but I don't have any quest for either of them and the skyrim wiki doesn't say what to do with these two books. What quests are these for?

One is for the book guy in the college of interhold and one is for the bards college.

For arcano restored I believe that is a book the mage college librarian will want. And for King Olaf's verse go speak with the bards college in solitude...they will be needing your help with that book.