I'm really lost on these ones

(a) suppose f and g are continuous functions on [a,b] such that $\displaystyle \int_a^b f = \int_a^b g$. Prove that $\displaystyle \exists x \in [a,b]$ such that f(x)=g(x)

(b) suppose f is an integrable function on [a,b] and suppose that g is a function such that f(x)=g(x) except forfinitelymany $\displaystyle x \in [a,b]$. Show that g is integrable on [a,b] and $\displaystyle \int_a^b f = \int_a^b g$