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It really depends on HOW you want to integrate it.
DaybackOnline, where you can publish the contents of your filemaker database onto a web based calendar URL, can be setup in as little as an hour.
Basic integration inside of filemaker, where you are loading the calendar and linking it to scripts inside of filemaker, is around 5-10 hours.
If clients want customization on top of the basic integration (custom CSS themes, enabling/disabling components, changing labels or making it multilingual) can balloon the developer time exponentially into many hours.
Best approach is to itemize the needs, and estimate based on that. So the answer to your question is between 1hr and "how much time/money do you have"?