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Bash and ksh93 you can use (( )).

if (( ex_year >= curr_year && ex_month >= curr_month && ex_day <= curr_day ))
then
condition...
fi


This work in every sh, dash,...

You don't say what shell you're using and it makes a big difference. With a shell conforming to the standards, the following will work:
if [ "$ex_year" -ge "$curr_year" ] && [ "$ex_month" -ge...