They found out during the day that Ramadan had begun, so they fasted

 

Some of our Muslim brothers did not know that Ramadaan had begun until after the sun had risen, but they completed their fast. Is that sufficient or do they have to repeat their fast?.

Praise be to Allaah.
 

 

They have done the right thing by refraining
from eating etc for the rest of the day, but they have to fast another day in its stead. 

Standing Committee for Academic Research and
Issuing Fatwas, 10/245 

The reason why they have to make up the fast
is that they did not have the intention of fasting from the night before. The Prophet (peace and blessings of Allaah be upon him) said:
“Whoever does not make the intention before dawn, there is no fast for him.” 

Narrated by Ahmad, 6/287; Abu Dawood, no.
2454; al-Tirmidhi, 730; al-Nasaa’i, 2331; classed as saheeh by al-Albaani in Saheeh Abi Dawood, 2143.