## What you’ll learn to do: Interpret definite integrals

In the preceding section we defined the area under a curve in terms of Riemann sums:

$A=\underset{n\to \infty }{\lim} \displaystyle\sum_{i=1}^{n} f(x_i^*)\Delta x$.

However, this definition came with restrictions. We required $f(x)$ to be continuous and nonnegative. Unfortunately, real-world problems don’t always meet these restrictions. In this section, we look at how to apply the concept of the area under the curve to a broader set of functions through the use of the definite integral.