May 23, 2018

$9$

#### Explanation:

graph of $f \left(x\right) = | x - 3 |$:
graph{|x-3| [0, 6, -5, 5]}

${\int}_{0}^{6} | x - 3 | \mathrm{dx}$ is the area between this graph and the x-axis:

while you can use integration, this problem seems to be easier to solve using geometry.

the area is two triangles. both of them have a width of 3 and height of 3.

area = $3 \cdot \frac{3}{2} + 3 \cdot \frac{3}{2} = 9$