Need some help with complex functions... :(

hello :D

I'm having big problem with simple issue, so if any one is willing to guide me to the right approach I will be most grateful :D

my problem is with this task :D

"If complex function $\displaystyle f(z)$ is regular in the area $\displaystyle D\subset \mathbb{C}$ than it's also continuous on same defined area."

and I need to prove it :D but i can't even start it because if I assume that some function is regular that implies that function is continuous.... !?!??! I have no clue how to do this :D