The definite integral of a function over an interval $[a, b]$ represents the net area under the curve of the function from $x = a$ to $x = b$. It is denoted by $\int_{a}^{b} f(x) \, dx$ and is calculated as the limit of Riemann sums.
Riemann Sum: An approximation of a definite integral by summing up areas of rectangles with heights determined by function values at specified points within subintervals.
Antiderivative: A function whose derivative is equal to the original function; used in evaluating definite integrals via the Fundamental Theorem of Calculus.
Trapezoidal Rule: A numerical method to approximate a definite integral by summing up areas of trapezoids formed under a curve.