Answer
FALSE
Work Step by Step
Consider $f(x)=\frac{|x|}{x}$
Then
$\int _{-1}^{1} f(x) dx=\int _{-1}^{1} \frac{|x|}{x}dx$
$\int _{-1}^{1} \frac{|x|}{x}dx=\int _{-1}^{0}(-1)dx+\int _{0}^{1} (1)dx$
$=(-x) _{0}^{1} +(x) _{0}^{1} $
$=-1+1$
$=0$
Here, the function $f(x)=\frac{|x|}{x}$ has only one jump discontinuity , that is at $x=0$
