In many modern treatments, integration is presented merely as “antidifferentiation,” that is, as the inverse of differentiation. The original geometric problem of determining an area is thereby transformed into a purely algebraic, algorithmic procedure, and much of the intuitive, visual understanding is lost. In this chapter, we present and analyze the methods of integration that Pierre de Fermat (1601–1665) developed for power functions. We show that Fermat’s second method, in particular, possesses considerable potential and can be extended to classes of functions that Fermat himself did not treat. The first method still appears occasionally in school and university textbooks. By contrast, the second method has largely fallen into obscurity and survives mainly in historical accounts. As we demonstrate, however, it retains a powerful and largely unexplored capacity to handle a broader range of functions than those originally considered by Fermat.