Lots of schools break up calculus in different ways, and that's fine. My school (and the schools of lots of people I know) break calculus up into calc 1, which is limits, differentials, and a toe dipping into integrals. Calc 2 is the 8 or so different tools for integrating progressively more difficult integrals. Calc 3 is multivariate calculus.
Lots of people have a very difficult time with calc 2. It feels very plodding- calc 1 and calc 3 (and diff eq and lin alg...) felt like I was learning new insight every week, calc 2 just felt like memorizing new vocabulary words. It wasn't just that it was hard, it was that it was hard and boring.
(obviously if a school breaks calc up differently your experiences will probably be different)
