$f\left(x\right)\stackrel{\frac{d}{dx}}{\to }{f}^{\prime }\left(x\right)\stackrel{\int }{\to }f\left(x\right)$

 

$f\left(x\right)=x$

$f^{\prime }\left(x\right)=1$

$\int f^{\prime }(x)dx=\int 1dx=x+C$

$f^{\prime }\left(x\right)={\left(x+C\right)}^{\prime }={\left(x\right)}^{\prime }+{\left(C\right)}^{\prime }=1+0=1$

 

$\int f(x)dx=F(x)$

$F^{\prime }\left(x\right)=f\left(x\right)$