It depends on what kind of integration you want.
The easiest is to use something called LTI (learning tools inter-operability). This allows a student to login to a JupyterHub setup through their LMS and have credentials (name, email, etc) provided by the LMS.
The challenge here is that students would need to access JupyterHub "through" the LMS.
LTI provides other capabilities such as passing back grades, etc but I don't think this extension does any of that.
I couldn't find much info on Quercus but most LMS's support LTI, including Canvas, Moodle, EdX, etc. Details in the github repo for setting it up.