Answer
$0$
Work Step by Step
$f(x)=\displaystyle \frac{x}{1+|x|},$
$f(-x)=\displaystyle \frac{-x}{1+|-x|}=-\frac{x}{1+|x|}=-f(x)$
The integrand is an odd function (there is symmetry in relation to the origin).
On one side of the y axis, the graph is below the x-axis, and on the other side, it is above x.
So, on the interval $[-3,3]$ the sum of the areas beneath the graph is 0.
