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Differentiate w.r.t. x
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\int x^{2}-1\mathrm{d}y
Evaluate the indefinite integral first.
\left(x^{2}-1\right)y
Find the integral of x^{2}-1 using the table of common integrals rule \int a\mathrm{d}y=ay.
\left(x^{2}-1\right)\times 3-\left(x^{2}-1\right)
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.
-2+2x^{2}
Simplify.