So I am doing a assignment which is to connect to a database and do operations on it. For that  I have chosen sqlite3 and for connecting to the database I found the ODBC driver for python is pyodbc.
My questions are, what is the difference between using pyodbc and doing it using the library sqlite3, i.e., import sqlite3 ? And is the pyodbc driver integrated in sqlite3?
The big advantage of using Python's built-in sqlite3 module is that it is built-in; there are no other dependencies. If your app uses pyodbc and SQLite ODBC then both of those external components must be available for the application to function.
If this is a personal project then you can obviously install what is necessary, but if this is ever going to be widely deployed then you will need to deal with the additional requirements if you choose pyodbc. Specifically, your [Python] app can register a dependency on pyodbc such that pip install your_app also installs pyodbc, but it cannot (practically) accommodate the requirement for the SQLite ODBC driver automatically so your installation instructions will need to address that.

And is the pyodbc driver integrated in sqlite3?

No. The SQLite ODBC driver is completely separate from both Python [sqlite3] and pyodbc.
Pyodbc and sqlite3 differences