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Evaluate
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Differentiate w.r.t. t
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\int 4\mathrm{d}t+\int -t^{2}\mathrm{d}t
Integrate the sum term by term.
\int 4\mathrm{d}t-\int t^{2}\mathrm{d}t
Factor out the constant in each of the terms.
4t-\int t^{2}\mathrm{d}t
Find the integral of 4 using the table of common integrals rule \int a\mathrm{d}t=at.
4t-\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}. Multiply -1 times \frac{t^{3}}{3}.
4t-\frac{t^{3}}{3}+С
If F\left(t\right) is an antiderivative of f\left(t\right), then the set of all antiderivatives of f\left(t\right) is given by F\left(t\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.