Some departments require you to use two quarters of Calculus to satisfy this requirement, including: all science majors, Economics, Psychology, Public Policy, and others. Check this by looking at the major’s requirements in the College Catalog; if specific courses are required to satisfy Core requirements, they will be listed under the program’s “Summary of Requirements” under a “General Education” category (example: Economics). In some cases the third quarter of the Calculus sequence is required for the major and would then be listed under the "Major" category. The first two quarters of Calculus are also required for pre-med requirements. See “Determining appropriate placement in Calculus,” below, to figure out which Calculus course is right for you.
If you're certain that you don't want to major in anything that requires Calculus, see "Non-Calculus Options," below.
If you're undecided but there's a chance you might be interested in something that requires Calculus, you should go ahead and take the appropriate Calculus course. The first two quarters of Calculus will satisfy the Mathematics requirement of Core even if you end up in a major that doesn't specify how you are to complete it, so you'll be set either way.