What does the definite integral introduction primarily cover?

The correct choice focuses on the basic principles of definite integration, where the concept revolves around calculating the exact area under a curve between two specified points on the x-axis. Definite integrals are represented with upper and lower limits of integration and are essential for determining the total accumulated quantity, such as area, volume, or other applications in physics and engineering.

In this context, understanding that definite integrals not only yield a numerical result but also embody fundamental ideas such as the concept of limits, summation, and the Fundamental Theorem of Calculus is crucial. This theorem connects differentiation and integration, underscoring how definite integrals can be evaluated using antiderivatives.

While the other suggestions, such as the concept of indefinite integration, history of integration techniques, and step-by-step instructions for solving integrals, are relevant to the broader subject of integration, they do not specifically encapsulate the focus of the definite integral introduction. This introduction primarily emphasizes the principles that define and govern how definite integrals work and why they are significant in mathematics and applied sciences.