Is incrementing a field in MySQL atomic?

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The write is atomic but an increment also requires a read. So the question is: Are you sure the read is safe, in other words, are you sure another thread doing the increment will not end up with the same value to be incremented? I have doubts. The 100% correct way of doing this would be.

-- begin transaction here

select counter from myCounters where counter_id = 1 FOR UPDATE;

-- now the row is locked and nobody can read or modify its values

update myCounters set counter = ? where id = 1;

-- set ? to counter + 1 programmatically

commit; -- and unlock...

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