The correct arm-swing is back and forth motion that is straight like a pendulum. There are a couple of common things that a lot of bowlers do instead, which can adversely affect the result of their delivery.
A significant percentage of bowlers to want to hold the bowling ball in the middle of their chest when they're in the stance. You're forced to move your arm sideways and back around your body for the back-swing if the ball is this far inside. This will throw everything out of whack.
Instead, hold the ball out to the side of your body (on the same side as your bowling hand) so you can swing straight back and forth.