What does those square brackets mean?

Question

While reading an article online, I encountered this expression.

I was wondering if anyone knows what does the square brackets in this expression do?

Thank you.

Answer 1

If $f:A \to B$ is a function and if $a \in A$ then $[f(x)]_{x=a}$ simply means $f(a)$.

Answer 2

What if the bracket is inside an integral? Or with a cipher or varible at the top and bottom see https://en.wikipedia.org/wiki/Integration_by_parts. But what else can it mean in calculus? Can it also mean a derivation?