One operation answers "how fast is this changing right now?" The other answers "how much has piled up so far?" Engineers move between them constantly because they're exact opposites of each other.
Almost every quantity an engineer tracks — position, charge, temperature, cost — can be looked at two different ways. You can ask how fast it's changing at this exact instant, or you can ask how much of it has built up over some stretch of time or space. The first question is a derivative. The second is an integral. They aren't two separate topics that happen to share a textbook chapter — they are inverse operations, and knowing which direction a problem is asking you to run in is half of solving it.