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It is common to see, in the books on calculus, primitives of functions (some authors use the word "antiderivative" instead of primitive). However, the majority of authors pay scant attention to the domains over which the primitives are valid, which could lead to errors in the evaluation of definite integrals. In the teaching of calculus, in particular, in the teaching of the substitution method, it is necessary to pay careful attention to the domains of functions, especially when trying to evaluate definite integrals by finding primitives. It turns out that the evaluation of definite integrals may require partitioning the interval of integration. This article attempts to do this for rational functions involving sin x and cos x, and may be of interest to strong undergraduate mathematics majors.