let $A = [ a_1 \dots a_n ]$ be a sorted list of integers of length $n$. By a simple algorithm that works in-place and in linear time we can remove all duplicates and output a sorted list of unique integers that are precisely the integers which appear .
More generally, it suffices to have a list with the promise that all identical integers are merely grouped to apply the same idea.
Now let $A$ be a list of integers, neither sorted nor even grouped as above. Let us call the problem of outputting a not-necessesarily sorted list of integers that are precisely the integers appearing $A$ by the term "uniquing problem".
An algorithm to solve the "uniqueing problem" might sort the list and remove multiple entries in the obvious way, thus requireing a running time of O( n log(n) ). Can we do better? I don't think so, although there might be a speed up because we actually do not require any sorting on the output list, so this algorithm performs actually too much.