I'm trying to realize a calculator using JAVA, so I'm following these stages:
for Unit testing I'm using JUnit but I don't know what I'm gonna need to accomplish the fifth stage.
i would say that 'integration' test should check how does your js code 'integrate' with rest of the application. that is if it sends and receives correct messages to/from backend, if it communicates correctly with browser storage etc. What you describe looks like a unit test
definition is quite good, according to International Software Testing Qualifications Board (ISTQ) syllabus : istqb.org/downloads/syllabi/foundation-level-syllabus.html /echatspin /echatrandom
i don't know nightwatch but according to their page
Nightwatch.js is an easy to use Node.js based End-to-End (E2E) testing solution for browser based apps and websites
it should get the job done