If you are intent on doing something, you are determined to get it done. If you have an intent, you have a motive or purpose.
Intention and intent are synonyms, but with a subtle difference. Intention implies a general desire or plan to accomplish something, while intent is a little stronger, indicating a firm resolve to get it done. Intent can be used as a noun or adjective. So you may be intent on finishing your homework, but the amount of it has you convinced of your teacher's ill intent.