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\int \frac{3x^{2}}{7}\mathrm{d}x
Evaluate the indefinite integral first.
\frac{3\int x^{2}\mathrm{d}x}{7}
Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.
\frac{x^{3}}{7}
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{2}\mathrm{d}x with \frac{x^{3}}{3}.
\frac{2^{3}}{7}-\frac{1^{3}}{7}
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.
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Simplify.
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