In the present paper it is shown that real function $g(x)=\int_{0}^{x}f(t)dt$is a linear-space computable real function on interval $[0,1]$ if $f$ is alinear-space computable $C^2[0,1]$ real function on interval $[0,1]$, and thisresult does not depend on any open question in the computational complexitytheory. The time complexity of computable real functions and integration ofcomputable real functions is considered in the context of Ko-Friedman modelwhich is based on the notion of Cauchy functions computable by Turing machines. In addition, a real computable function $f$ is given such that$\int_{0}^{1}f\in FDSPACE(n^2)_{C[a,b]}$ but $\int_{0}^{1}f\notin FP_{C[a,b]}$if $FP\ne#P$.
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机译：在本文中，实函数$ g（x）= \ int_ {0} ^ {x} f（t）dt $是间隔$ [0,1] $上的线性空间可计算实函数，如果$ f $是区间$ [0,1] $上的线性空间可计算$ C ^ 2 [0,1] $实函数，并且此结果不依赖于计算复杂性理论中的任何开放性问题。在Ko-Friedman模型的上下文中考虑了可计算的实函数的时间复杂性和可计算的实函数的集成，该模型基于Turing机器可计算的柯西函数的概念。另外，给出了真实的可计算函数$ f $，使得FDSPACE（n ^ 2）_ {C [a，b]} $中的$ \ int_ {0} ^ {1} f \但$ \ int_ {0} ^ {1} f \ notin FP_ {C [a，b]} $ if $ FP \ ne＃P $。
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