When I write Java-projects that produce web pages, I test on several levels. First, I use Jetty and WebDriver to test the result via http. (WebDriver even lets me test JavaScript!)
But for speed and agility, unit-level tests beat even the fastest integration level tests. Unit tests run much much faster, and lets me pinpoint problems much more accurately. As a general rule: If you introduce a bug, you want a unit test to be the one that sees it first.
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