Integral formulas are mathematical expressions that represent the relationship between integrals and functions. They are used to calculate the area under curves, find accumulated quantities, and solve problems in various fields such as physics and engineering. Common integral formulas include the Fundamental Theorem of Calculus, which connects differentiation and integration, and specific formulas for calculating the integrals of basic functions. These formulas can simplify complex calculations by providing standard results for common integrals. For example, the integral of sin(x) is -cos(x), and the integral of e^x is e^x. Mastering these formulas is essential for solving more advanced problems in calculus and analysis.