

I do understand it differently, but I don’t think I misunderstood. I think what they meant is the physicist notation I’m (as a physicist) all too familiar with:
∫ f(x) dx = ∫ dx f(x)
In this case, because f(x) is the operand and ∫ dx the operator, it’s still uniquely defined.
Also related, I had a psychology teacher with a PhD in psychology. But because in German schools, you need to teach two subjects (with the exception of the arts), he also taught physics. He was a terrible physics teacher, but a pretty good psychology one.