When the parties to a contract express their agreement in a writing that is deemed an "integration" of their agreement, how will a court deal with evidence of other written or oral expressions relating to the bargain?

Helen tells her nephew, bernard, that she will pay him $100 if he will stop smoking for six months. helen was hopeful that if bernard stopped smoking for six months, he would stop altogether. bernard stops smoking for six months but then resumes his smoking. helen will not pay him. she says that the type of promise she made cannot constitute a binding contract and that, furthermore, it was at least implied that he would stop smoking for good. can bernard legally collect $100 from helen