#### To determine

The given statement is true or false.

#### Answer

False

#### Explanation

Recall if fx≥0, the integral ∫abf(x) dx is the area under the curve y=f(x) from a to b

If some part of f(x) lies below x-axis that is fx≤0 for some x in the interval then the integral ∫abf(x) dx is the net area

Consider the integral,

∫02x-x3dx

Here, function fx<0 for 1<x≤2

So,∫02x-x3dx does not represent the area under the curve. It represents net area (that is area of the region above x-axis minus that below the x-axis).

So, the given statement is false.

**Conclusion:**

The given statement is false.