### Introduction

Before diving into calculus and memorizing formulas, it is important to take a step back and understand what an integral actually means.

### What is an Integral?

An integral, graphically, represents the **area under a curve**. You might be wondering why it’s useful to know the area under the curve. The reason is that the area under the curve represents the **accumulation** of the quantity described by the function over an interval.

For example, if we have a simple graph that charts book sales per hour, the integral of that graph, or area under the curve, gives the **total number of books sold** over a period of time. By looking at the rate of sales, we can find the total accumulation of sales.

### Applications in Physics

This concept has many applications, one of the most common being in physics. Velocity is the rate of change of distance. The area under the velocity-time curve represents the **total distance traveled**.

Suppose \( v(t) \) represents velocity as a function of time. Then the distance \( s \) traveled from time \( t = a \) to \( t = b \) is:

\[\begin{align*} s = \int_{a}^{b} v(t) \, dt \end{align*}\]

By calculating this integral, we sum up all the small distances covered over each infinitesimal time interval between \( a \) and \( b \).

### Conclusion

Understanding integrals as the area under a curve allows us to solve real-world problems involving accumulation, such as calculating total sales, distance traveled, or any other quantity that accumulates over time.