Evaluate
\frac{1}{2}=0.5
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\int _{0}^{1}\frac{x\left(x-1\right)\left(-x-1\right)}{\left(x-1\right)\left(-x-1\right)}\mathrm{d}x
Factor the expressions that are not already factored in \frac{x-x^{3}}{1-x^{2}}.
\int _{0}^{1}x\mathrm{d}x
Cancel out \left(x-1\right)\left(-x-1\right) in both numerator and denominator.
\int x\mathrm{d}x
Evaluate the indefinite integral first.
\frac{x^{2}}{2}
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x\mathrm{d}x with \frac{x^{2}}{2}.
\frac{1^{2}}{2}-\frac{0^{2}}{2}
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.
\frac{1}{2}
Simplify.
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