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\int T^{2}\mathrm{d}T
Evaluate the indefinite integral first.
\frac{T^{3}}{3}
Since \int T^{k}\mathrm{d}T=\frac{T^{k+1}}{k+1} for k\neq -1, replace \int T^{2}\mathrm{d}T with \frac{T^{3}}{3}.
\frac{5^{3}}{3}-\frac{2^{3}}{3}
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.
39
Simplify.
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