To teach at the college level (or at a private high school), a minimum of a master's degree in mathematics (or a closely related field) is required. Some colleges will allow teachers to teach as adjuncts (meaning they are not official professors, do not have offices, teach only a few classes, and make a much lower salary than official professors) if they are in the process of getting a master's degree.
To teach at the high school level, the requirements vary from state to state in the US. Most require a bachelor's degree in mathematics education.
The main difference is that colleges do not require any education background whatsoever (just math) while high schools require more education than math (in some districts with a shortage of teachers, a history teacher with no math background could be allowed to teach calculus).
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Calculus is not regularly required for college.Specifically, if you want to be certain, every college has its own courses that are mandatory. If calculus is not one of them, you're in. However, as well, if you already have a major, visit the department at the college you are in.Ask the department which courses are required for your major. And that should be all.
These are the general math courses in an undergraduate program of Mechanical Engineering. Actually, these are also the math courses required in ANY undergraduate Engineering curriculum: Algebra Trigonometry Analytic Geometry Differential Calculus Integral Calculus Mutivariable Calculus Differential Equations
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.