1. The integral is a fundamental concept in calculus used to find the area under a curve or the accumulation of quantities. 2. There are two main types: definite integrals and indefinite integrals. 3. An indefinite integral represents a family of functions and is written as $$\int f(x)\,dx = F(x) + C$$, where $F'(x) = f(x)$ and $C$ is the constant of integration. 4. A definite integral calculates the area between the curve $y = f(x)$ and the x-axis from $a$ to $b$, represented as $$\int_a^b f(x)\,dx$$. 5. Integration is the reverse process of differentiation and has many applications in physics, engineering, and probability.