I think that you should retake 31A if you don't know how to differentiate.
Getting a 1 or 2 in Calculus BC is pretty poor performance .. that means you scored below 50% on the Calculus AB(!) and BC concepts and don't have a solid grasp of calculus concepts. You should refresh your knowledge of the different methods to integrate, and what situation is the best to use which method. If you do that, I think you should be prepared to take 31B. A lot of people have good backgrounds coming into 31B, just to warn you.
Although, depending on your prospective major, only the core of the calculus concepts are carried on in subsequent courses, they are extremely important in your critical and practical thinking development.
Basic skills from 31A and 31B will help you solve Bessel, Airy, Legendre, where integration becomes only one step in solve the ODE or PDE.