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=\int_{0}^{3} 5 t-t^{2} \mathrm{dt}=\frac{5}{2} t^{2}-\left.\frac{t^{3}}{3}\right|_{0} ^{3}=\left(\frac{5}{2} \cdot 9-\frac{27}{3}\right)-\left(\frac{5}{2} \cdot 0-\frac{0}{3}\right)=13 \frac{1}{2}