Frequency warping when integrators are replaced with backward-euler and forward-euler integration
To the extent this helps, here are some interesting magnitude and phase plots of the backward Euler (here using the method of impulse invariance mapping which for 1/s has the same result as backward Euler but as Matt L points out in the comments is not generally the case) vs Tustin (method of Bilinear Transform mapping) integrators. Notice the Euler on the left has dominant phase distortion while the Tustin on the right has more dominant amplitude distortion (no phase distortion from an analog integrator at all!).

The analog frequency response for a pure integrator as $1/s$ is -20 dB/decade in magnitude ($1/f$) and -90° for phase.