I want to show that
Let f be bounded on [a,b]. If g is bounded on [a,b] and g(x)=f(x) for all but finitely many points in [a,b], then g is integrable on [a,b] and Then $$\int_a^b f=\int_a^b g$$
I have trouble understaing the meaning of the phrase "for all but finitely many". Does anyone can give me an answer or a hint?