A piecewise constant function.

Assume $f^{\text{'}}$ is given by the graph below. Suppose $f$ is continuous and that $f(3)=0.$

$($Click on the graph for a larger version.$)$

Sketch, on a sheet of work paper, an accurate graph of $f,$ and use it to find each of

$f(0)=$

and

$f(7)=$

Then find the value of the integral:

${\displaystyle \underset{0}{\overset{7}{}}}{f}^{\text{'}}(x)dx=$

$($Note that you can do this in two different ways!$)$