No it usually doesn't.
The calculus they expect you to know is generally first semester calculus with enough integration from the second semester. That sort of question is doable, but the question isn't doable without knowing the rule; they don't expect you to memorize rules to that sort of degree. Of course, if you did have it memorized you'd have the advantage, but you'd seriously only see 1 question like that on any given exam if any at all.