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=\lim _{\text {mesh } \rightarrow 0}\left(\sum_{k=1}^{n} f\left(c_{k}\right) \cdot \Delta x_{k}\right)+\lim _{m e s h \rightarrow 0}\left(\sum_{k=1}^{n} g\left(c_{k}\right) \cdot \Delta x_{k}\right)=\int_{\mathrm{a}}^{\mathrm{b}} \mathrm{f}(x) \mathrm{d} \mathrm{x}+\int_{\mathrm{a}}^{\mathrm{b}} \mathrm{g}(x) \mathrm{dx}