Recognizing opportunities to apply knowledge of geometry and mathematical rules can simplify integration. Determine antiderivatives of functions and indefinite integrals, using knowledge of derivatives. ∫f(x)dx is an indefinite integral of the function f and can be expressed as ∫f(x) dx = F(x) + C, where F′(x) = f(x) and C is any constant. Differentiation rules provide the foundation for finding antiderivatives. Many functions do not have closed-form antiderivatives.