Integrals are used to find the area or volume bounded by lines and can be definite or indefinite. There are several methods for solving integrals including the reverse power rule, substitution method, and evaluating definite integrals by substituting the bounds. Indefinite integrals are anti-derivatives with an added constant, while definite integrals substitute bounds to find the area between them. Position, velocity and acceleration are related through anti-derivatives.