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Differentiate w.r.t. x
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\int x\mathrm{d}x+\int -2\mathrm{d}x
Integrate the sum term by term.
\frac{x^{2}}{2}+\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\mathrm{d}x with \frac{x^{2}}{2}.
\frac{x^{2}}{2}-2x
Find the integral of -2 using the table of common integrals rule \int a\mathrm{d}x=ax.
\frac{x^{2}}{2}-2x+С
If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.