Answer
negative
Work Step by Step
Apply Th.4.6 from section 4-3, Additive lnterval Property
$\displaystyle \int_{-2}^{2}f(x)dx=\int_{-2}^{0}f(x)dx+\int_{0}^{2}f(x)d$,
graphing the integrand function ( image below) we estimate that
the two definite integrals on the RHS, each representing an area, are such that
the area below the x-axis is greater in magnitude than the area above the x-axis.
The sum of integrals on the RHS is negative, so
the integral $\displaystyle \int_{-2}^{2}f(x)dx$
is negative
