Which principle is utilized when integration is approached as a limit of Riemann sums?

Integration, when approached as a limit of Riemann sums, fundamentally relies on approximating the area under a curve. This method involves dividing the area into smaller regions (typically rectangles), calculating the areas of these regions, and then summing these areas to estimate the total area under the curve. As the width of the subdivisions approaches zero, this sum converges to the exact area, which is the integral of the function.

The Riemann sum is a pivotal concept in defining the integral, particularly in understanding that the integral represents the accumulation of infinitesimally small quantities (in this case, the areas of the rectangles) as the number of rectangles increases and their width decreases. This principle allows us to define the definite integral as the limit of the Riemann sums, thereby providing a clear geometric interpretation of integration.

While the concept of antiderivatives and the inverse relationship between differentiation and integration are also important in calculus, they pertain more to the Fundamental Theorem of Calculus rather than the process of forming Riemann sums. The Fourier Transform property concerns a different area of analysis that relates to signals and frequencies, making it unrelated to the basic idea of integration as a limit of sums. Thus, the approach of integration through Riem