The
derivative of a constant term is 0, so when a term containing a constant term is differentiated, the constant term vanishes, regardless of its value. Therefore the
antiderivative is only determined up to an unknown constant term, which is called "the constant of integration" and added in symbolic form (usually denoted as C). For example, the antiderivative of \cos x is \sin x, since the derivative of \sin x is equal to \cos x based on the
properties of trigonometric derivatives. However, the
integral of \cos x is equal to \sin x (the antiderivative), plus an arbitrary constant: \int \cos x \, \mathrm dx = \sin x + C, because for any constant C, the derivative of the right-hand side of the equation is equal to the left-hand side of the equation. ==See also==