f,g are continues funtion on [a,b]

prove or desprove by counterexample that:

if $\displaystyle \int_{a}^{x}f(t)dt=\int_{a}^{x}g(t)dt$ then f=g on [a,b]

?

how i tried:

i this its correct

i transfered to the other side

$\displaystyle \int_{a}^{x}f(t)dt-\int_{a}^{x}g(t)dt=0$

$\displaystyle \int_{a}^{x}f(t)-g(t)dt=0$

what now?

i cant do derivative here

because if i could the i just could do a derivative on both sides from the start

but it looks to easy thus it is a wrong move.