If you use GNU find, since version 4.3.3 you can do:
find -newerct "1 Aug 2013" ! -newerct "1 Sep 2013" -ls
It will accept any date string accepted by GNU date -d.
You can change the c in -newerct to any of a, B, c, or m for looking at atime/birth/ctime/mtime.
Another example – list files modified between 17:30 and 22:00 on Nov 6 2017:
find -newermt "2017-11-06 17:30:00" ! -newermt "2017-11-06 22:00:00" -ls
Full details from man find:
-newerXY reference
Compares the timestamp of the current file with reference. The reference argument is normally the name of a file (and one of its timestamps is used
for the comparison) but it may also be a string describing an absolute time. X and Y are placeholders for other letters, and these letters select
which time belonging to how reference is used for the comparison.
a The access time of the file reference
B The birth time of the file reference
c The inode status change time of reference
m The modification time of the file reference
t reference is interpreted directly as a time
Some combinations are invalid; for example, it is invalid for X to be t. Some combinations are not implemented on all systems; for example B is not
supported on all systems. If an invalid or unsupported combination of XY is specified, a fatal error results. Time specifications are interpreted as
for the argument to the -d option of GNU date. If you try to use the birth time of a reference file, and the birth time cannot be determined, a fatal
error message results. If you specify a test which refers to the birth time of files being examined, this test will fail for any files where the
birth time is unknown.