If you want to extract log with prefix is date time like this
[2017-05-01 02:00:06,300] this is a log line details
We might use the awk command following with the condition
awk -F'[]]|[[]' '$0 ~ /^\[/ && $2 >= "2017-05-01 00:00" { p=1 } $0 ~ /^\[/ && $2 >= "2017-06-01 00:00" { p=0 } p { print $0 }' details.log > 2017-05.log