Answer:
Please check the explanation.
Step-by-step explanation:
Let us consider

To find the area under the curve
between
and
, all we need is to integrate
between the limits of
and
.
For example, the area between the curve y = x² - 4 and the x-axis on an interval [2, -2] can be calculated as:

=


solving


![=\left[\frac{x^{2+1}}{2+1}\right]^2_{-2}](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cfrac%7Bx%5E%7B2%2B1%7D%7D%7B2%2B1%7D%5Cright%5D%5E2_%7B-2%7D)
![=\left[\frac{x^3}{3}\right]^2_{-2}](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cfrac%7Bx%5E3%7D%7B3%7D%5Cright%5D%5E2_%7B-2%7D)
computing the boundaries

Thus,

similarly solving


![=\left[4x\right]^2_{-2}](https://tex.z-dn.net/?f=%3D%5Cleft%5B4x%5Cright%5D%5E2_%7B-2%7D)
computing the boundaries

Thus,

Therefore, the expression becomes



square units
Thus, the area under a curve is -10.67 square units
The area is negative because it is below the x-axis. Please check the attached figure.