By increasing the condition of the integral mean value theorem, we prove that the existence of intermediate point and the existence of interval are corresponding to each other.

给出了积分中值定理的一个注记，证明了中值点的存在性与覆盖中值点的区间的存在性是相互对应的。

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This article explores the four ways for solving integral inequality with the nature of definite integral, mean value theorem of differentials, Schwarz inequality and double integral.

本文利用定积分的性质、微分中值定理、施瓦兹不等式、二重积分等内容，研究了积分不等式的四种证法。

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Finally, the condition and result of integral mean-value theorem are also improved combined with the Lagrange mean value theorem of differentials.

最后，结合拉格朗日微分中值定理改进了积分中值定理的条件和结论。

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