Laurent Koscielny struck the winning goal at the start of the second half for the Gunners.
Tottenham beat Sunderland 1-0 thanks to a late Gareth Bale goal but it was not enough for fourth.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.