We generally use the prepositions "on" or "upon" after the adjective "intent" to express purpose.
We generally use the prepositions "on" or "upon" after the adjective "intent" to express purpose:
Everyone was intent on listening.
Are you intent upon destroying her reputation?
"Intent on", however, is much more common than "intent upon".
Source: Google Books Ngram Viewer
Olivia was intent on going to work even though she was sick.
On the other hand, we can use the preposition "to" when using "intent" as a noun in constructions like these:
It was not his intent to hurt anyone.
Note that you can replace "intent" by "intention" in the example above.
