What is a key property of definite integrals?

Definite integrals are used to calculate the net area under a curve over a specified interval. The key property highlighted in the correct choice emphasizes that definite integrals can yield a positive, negative, or zero value depending on the function being integrated and the limits of integration. This means that if the curve lies above the x-axis for most of the interval, the area will be positive. Conversely, if the curve lies below the x-axis, the area will be negative. When the curve crosses the x-axis, the integral may yield a value that is a combination of positive and negative areas, resulting in a net area that reflects this overall contribution.

This illustrates the nature of definite integrals as measuring the signed area, which is crucial in many applications in calculus, physics, and engineering, demonstrating not just the area but also the direction of the area with respect to the x-axis.

The other properties presented do not accurately reflect the characteristics of definite integrals; they can indeed be positive or negative based on the function and limits, but they are not restricted to being only negative or necessarily independent of the interval, nor do they only provide a fixed measure of area in a simplistic sense.