PID control is the classic example, but at a far enough abstraction any looping algorithm can be argued to be an implementation of the concepts underpinning calculus. If you're ever doing any statistical analysis or anything in game design having to do with motion, those are both calculus too. Data science is pure calculus, ground up and injected into your eyeballs, and any string manipulation or Regex is going to be built on lambda calculus (though a very correct argument can be made that literally all computer science is built of lambda calculus so that might be cheating to include it)

Graphics programming is the most obvious one and it uses it plenty, but really any application that can be modeled as a series of discrete changes will mostly likely be using calculus.

Time series data is the most common form of this, where derivatives are the rate of change from one time step to the next and integrals are summing the changes across a range of time.

But it can even be more abstract than that. For example, there's a recent-ish paper on applying signal processing techniques (which use calculus themselves, btw) to databases for the purposes of achieving efficient incremental view maintenance: https://arxiv.org/abs/2203.16684

The idea is that a database is a sequence of transactions that apply a set of changes to said database. Integrating gets you the current state of the database by applying all of the changes.

Computers are just big calculators so to program them you need calculus.

that can't be right. maybe they meant lambda calculus? programmers are definitely good at applied logic, graph theory, certain kinds of discrete math etc. but you're not whipping out integrals to write a backend.

Lotta infinite sums in loops

good physics/graphics engine require calculus

That sounds like it might be a gift in disguise.