Answer
f is integrable on [-1,1]
f has a discontinuity at x=0
Work Step by Step
Sample answer:
Set up a piecewise function, such as
$f(x)=\left\{\begin{array}{lll}
1, & & x < 0\\
2, & & x \geq 0
\end{array}\right.$
See image below,
f is integrable on [-1,1], $\displaystyle \int_{-1}^{1}f(x)=3$
and
f has a discontinuity at x=0
(f is not continuous on [-1,1] )
