Is it obligatory to fast and make up the day for one whose menstrual bleeding stopped after Fajr and who did not make the intention to fast from the night before?

The default is for menstruation to continue until certainty of purity is established. So, as long as you did not verify your purity until after the adhan, you are considered to be in the state of menstruation at the beginning of the day, and you became pure during the day. Therefore, your fast is not valid, and you must make it up. The jurists differ on the obligation to refrain from eating and drinking for the rest of the day. The Shafi'is and Malikis do not consider refraining obligatory, while the Hanafis and Hanbalis consider it obligatory. However, neglecting to perform ghusl (ritual bath) after menstruation does not prevent the fast.