1. Let's start by understanding what an integral is. 2. The integral of a function represents the area under the curve of that function between two points on the x-axis. 3. There are two main types: definite integrals and indefinite integrals. 4. An indefinite integral represents a family of functions and includes a constant of integration $C$. For example, $$\int x^n\,dx = \frac{x^{n+1}}{n+1} + C$$, where $n \neq -1$. 5. A definite integral calculates the exact area between limits $a$ and $b$, written as $$\int_a^b f(x)\,dx$$. 6. To compute an integral, identify the antiderivative of the function, then for definite integrals evaluate it at the upper and lower limits. 7. Example: Find $$\int_0^2 3x^2\,dx$$. 8. First, find the antiderivative of $3x^2$, which is $$x^3 + C$$. 9. Then evaluate from 0 to 2: $$2^3 - 0^3 = 8 - 0 = 8$$. 10. So, $$\int_0^2 3x^2\,dx = 8$$. 11. Integrals help in physics, engineering, and many fields to find quantities like area, volume, and accumulated change. 12. To practice, try integrating polynomial functions or simple trigonometric functions using these steps.