In this video, the first part of the fundamental theorem of calculus is discussed. It explains that if g(x) is the definite integral of f(t) from a to x, then the derivative of g(x) equals f(x). This concept highlights that the derivative of an antiderivative results in the original function. The video provides an example problem to illustrate this theorem, emphasizing the process of finding the antiderivative and evaluating it at specific values to determine the final answer. The explanation demonstrates how to apply the fundamental theorem of calculus in solving integration and differentiation problems, showcasing the relationship between antiderivatives and derivatives. The video encourages viewers to engage with a practice problem involving finding the antiderivative of a square root function. Overall, the video aims to deepen understanding of the fundamental theorem of calculus through practical examples and step-by-step explanations.