strange result loop exit status

[Dmitry Arkhireev]

Hello, I observe strange behavior in bash exit status
I=0; while [ $I -ne 1 ]; do ((I++)); done; echo $?
1

but
I=0; while [ $I -ne 0 ]; do ((I++)); done; echo $?
0

I=0; while [ $I -ne 2 ]; do ((I++)); done; echo $?
0

And if run it sample with echo $I after ((I++)) everything works as expected
I=0; while [ $I -ne 1 ]; do ((I++)); echo $I; done; echo $?
1
0


What I do wrong?