Not remembering U substitution of the top of your head is different than not being exposed to it. I remind you that Int(x^3 * 5x^2 + 7) == x^4/4 + 5x^3/3 +7x + C. Just from that alone I bet a lot of memories of integration slot back into your head, and you would know where to look up the parts you forgot.
You can’t “brush up” on something you never learned
It doesn't matter if you can't solve a randomly-appearing-in-your-newsreel integral; it matters that you have the background knowledge of what an integral is, that there are rules to solving it, and you can read up on the rules and understand them.
For the [current] layperson, each of those things I mentioned I might as well be speaking in Martian.
if you actually spent good amount of time in mathematics during academia, you have developed neural networks for logical reasoning and problem solving but they get activated in life situations giving an edge compared to others.
It's not necessarily just about remembering every rule and trick you can use to simplify and solve integrals. Calculus is fundamental to understanding problems, from basic exercises in a first-year undergraduate physics course to entire fields.
You'll (probably) never apply the ability out the kinetic energy vs. time of a ball rolling down a hill, but these exercises build understanding of the tools. Derivatives are everywhere in a fundamental electric circuits course, you need to have an intuitive understanding of basic calculus. The relationship between current through and voltage across ideal inductors and capacitors are directly described in the language of calculus, even if you're not "using" the calculus substitutions you learned each time you analyse a circuit.
And good luck getting through a couple weeks of an introductory quantum mechanics course without using calculus as a fundamental building block. You can solve many of these problems with computers, but it's not going to build intuition on how to approach future problems. (I don't mean this as a joke or picking an arbitrary complicated-sounding topic; this is a core course in some engineering programs.)
Many engineering problems have nice closed-form equations (at least to get approximations). Obtaining those equations often involves calculus, and someone has to do that in the first place.
(I'm giving examples from the lens of my education, but each field of science, engineering, and mathematics will have their own context, and will vary from little-to-no calculus to being all-calculus.)
You can’t “brush up” on something you never learned