Date is not an integer, at least as far its practical use is concerned.
Now, as for the lecture, professor was mentioning about a workaround. So, if you're dealing with a single year, you could indicate each date as an integer. 1-Jan as 0, 2-Jan as 1...31-Dec as 364.
However, pls note this isn't always a practical solution, since you'll typically deal with multiple years as part of your data. If you've to represent the birthdate of a person, you'll not able to use this technique, since there's no way to represent the year.