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Question Number 215386 by JasonHidd last updated on 04/Jan/25

Answered by mr W last updated on 04/Jan/25

$${\int }_0^{x}f\left(x\right)dx={\underset{0}{\int }}^{-x}f\left(x\right)dx+{\int }_{-x}^{x}f\left(x\right)dx$$$$thisisalwaystrue.$$$$nowthequestionisiff\left(x\right)existss.t.$$$${\int }_0^{x}f\left(t\right)dt=x^2+2x+1$$$$theanswerisno.$$$$sayF\left(x\right)={\int }_0^{x}f\left(t\right)dt$$$$F\left(0\right)={\int }_0^{0}f\left(t\right)dt=0$$$$butF\left(x\right)=x^2+2x+1\Rightarrow F\left(0\right)=1\ne 0.$$

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