This is dialogflow nodejs fulfillment webhook sample.
The end point url lcoalhost:3001/webhook(use ngrok to get public url), enter this value in fulfillment webhook url in api.ai this takes the request and gives the json fulfillment json response of last 10 calendar events back to dialogflow
#Google Calendar API
generate the credentails and token using the following google calendar nodejs example
https://developers.google.com/calendar/quickstart/nodejs
update you the in the eventlist with your calendar id and enjoy...