Taylor series but with integral

 Motivation: $$\exp\left(\int_a^b\cdot dx\right)f(x)=?$$

Wandering:

$$f(x)\Big|_{x=x_0}=f(x_0)+(x-x_0)\int_{0}^{x_0}f(\chi)d\chi + \frac{(x-x_0)^2}{2}\int_{0}^{x_0}\left(\int_{0}^{\xi}f(y)dy\right)d\xi+\cdots$$