Calculus was invented independently by Isaac newton and Gottfried Leibnitz. Newton did it first and showed the actual usefulness of the discipline by deriving the Law of gravity from astronomical data. Leibnitz however developed a much superior notation and terminology, thus it is actually Leibnitz's calculus that we use today.
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Leonhard ''Euler''
Calculus; by a long shot.
Just about all of calculus is based on differential and integral calculus, including Calculus 1! However, Calculus 1 is more likely to cover differential calculus, with integral calculus soon after. So there really isn't a right answer for this question.
It is certainly used in calculus, just as calculus can be used in trigonometry.