Beyond calculating just as an exercise, are there any other reasons to calculate an indefinite integral? Calculus textbooks often have us calculate indefinite integrals as exercises.  However, beyond calculating just as an exercise, are there any other reasons to calculate an indefinite integral?

I am guessing you want to emphasize solving indefinite integrals vs. definite integrals. To state the obvious, if you don't know how to do the former, you won't be able to do the latter. So there's a good reason.
Beyond that evaluating indefinite integrals is key to solving many important differential equations.  ('Important' here means a few things, including many applications.)
