As far as I know, Integrated 3 would require precalculus then Calculus but some integrated math classes allow students to skip precalculus, some HS treat AB and BC as separatz courses where AB is slower whereas some HS treat AB as one level and BC as the second level.
Can you list ALL the classes that that be taken after 3AB at your school?
What were your grades in Integrated 2? 3 A? 3 B?