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\int _{-1}^{1}0\mathrm{d}x
Combine e^{x} and -e^{x} to get 0.
\int 0\mathrm{d}x
Evaluate the indefinite integral first.
0
Find the integral of 0 using the table of common integrals rule \int a\mathrm{d}x=ax.
0+0
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
0
Simplify.