The Integral Program is based on the Great Books Program at St. John's College. It's a 4 your course, and Integral Program is your major. You have to start the program as a freshman as it is sequential in nature. No exams, it's tons of reading, discussion and essay writing. Did you find this link? About
Also, if you look up the St. John's website (either Santa Fe or Annapolis), you can get a good idea of what a great books program is all about.
Don't know anything about the Honors Program, the freshman I know who entered with honors a couple years ago took additional classes and lived in the honors dorm, which does offer some additional activities and lectures.