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\int x^{3}-2\mathrm{d}x
Evaluate the indefinite integral first.
\int x^{3}\mathrm{d}x+\int -2\mathrm{d}x
Integrate the sum term by term.
\frac{x^{4}}{4}+\int -2\mathrm{d}x
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{3}\mathrm{d}x with \frac{x^{4}}{4}.
\frac{x^{4}}{4}-2x
Find the integral of -2 using the table of common integrals rule \int a\mathrm{d}x=ax.
\frac{3^{4}}{4}-2\times 3-\left(\frac{1^{4}}{4}-2\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.
16
Simplify.