I was studying integrals and just out of curiosity,
Does there exist any 'continuous' functions such that $\int_a^af(x) \, dx$ ($a$ is any number) equals a value other than $0$?
Since continuous functions are Riemann integrable, so I think it should be $0$. Is this correct?
Also, with out the condition 'continuous', does there exist any function such that $\int_a^af(x) \, dx$ isn't $0$?
I'm looking for any function that $\int_a ^a\ f(x) \neq 0$. Can anyone find me one?