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{\displaystyle \int \limits _{a}^{a}f(x)dx=0}
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{\displaystyle \int \limits _{a}^{b}f(x)dx=-\int \limits _{b}^{a}f(x)dx}
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{\displaystyle \int \limits _{a}^{b}f(x)dx=\int \limits _{a}^{c}f(x)dx+\int \limits _{c}^{b}f(x)dx}
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{\displaystyle \int \limits _{a}^{b}[f(x)\pm g(x)]dx=\int \limits _{a}^{b}f(x)dx\pm \int \limits _{a}^{b}g(x)dx}
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{\displaystyle \int \limits _{a}^{b}kf(x)dx=k\int \limits _{a}^{b}f(x)dx}
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{\displaystyle \int \limits _{a}^{b}ndx=nx=nb-na=n(b-a)}
![{\displaystyle \int \limits _{a}^{b}[f(x)\pm g(x)]dx=\int \limits _{a}^{b}f(x)dx\pm \int \limits _{a}^{b}g(x)dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c5de6f389f5d8d17cc73712d5d510feb29c3cdf3)
