Why are there 31 days in the month of August?

According to a popular legend, July was named after Julius Ceaser , hence it had 31 days. But when Augustus became an empreor, he wanted to overshedow the deeds of his predecessor Julius Ceaser. To this end, Augustus decided that the eight month of the year be named after him. Prior to the foregoing, the 8th month had only 29 days, but in order to measure up with the number of days in July which was named after Julius Ceaser, the ambitious Augustus removed two days from February and added same to August thus the 31 days we today have in August and the 28 days in February. Thank God for democracy, those emperor guys were stupendously powerful.