Which of the following best describes the role of limits in definite integrals?

The correct choice highlights that limits in definite integrals specifically serve to establish the boundaries for the calculation of area under a curve. In the context of definite integrals, the limits are the values that define the interval over which the integration occurs. For instance, when evaluating the integral of a function from (a) to (b), (a) and (b) are the lower and upper limits, respectively. The definite integral (\int_{a}^{b} f(x) , dx) represents the exact area between the curve (y = f(x)), the x-axis, and the vertical lines (x = a) and (x = b). This area can be positive, negative, or even zero, depending on how the function behaves across the specified interval.

The role of limits is fundamental in this process, as they demarcate the start and end points for the accumulation of area, clearly defining the scope of the integral. The boundaries provided by these limits are essential for obtaining the numerical value of the integral, which represents the net signed area under the curve.

While other choices touch on relevant concepts in integration, they do not accurately capture the specific role played by limits in the context of definite