I'm using the textbook Electricity and Magnetism by Purcell. In the section about continuous charge distributions I found the following formula
\mathbf{E}(x,y,z)= \frac{1}{4\pi\epsilon_0 } \int \frac{\rho(x',y',z')\boldsymbol{\hat r} dx'dy'dz'}{r^{2}} .
It's stated that (x,y,z) is fixed...