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\begin{aligned} &\int_{5}^{7} \mathrm{~g}(x)-\mathrm{f}(x) \mathrm{dx}=\int_{5}^{7}\left(x^{2}-4 x+3\right)-(x+3) \mathrm{dx}=\int_{5}^{7} x^{2}-5 x \mathrm{dx}=\frac{x^{3}}{3}-\left.\frac{5}{2} x^{2}\right|_{5} ^{7}=12 \frac{4}{6} \end{aligned}