1. Straight out of the HS rule book:
SECTION 11 CONTINUOUS MOTION

ART.1...Continuous motion applies to a try or tap for field goals and free throws, but it has no significance unless there is a foul by the defense during the interval which begins when the habitual throwing movement starts a try or with the touching on a tap and ends when the ball is clearly in flight.

ART.2...If an opponent fouls after a player has started a try for goal, he/she is permitted to complete the customary arm movement, and if pivoting or stepping when fouled, may complete the usual foot or body movement in any activity while holding the ball.

2. Straight out of the NCAA rule book:
SECTION 14. Continuous Motion

Continuous motion applies to a try or tap for field goals or free throws, but it has no significance unless there is a foul by the defense during the interval which begins when the habitual throwing movement starts a try or with the touching on a tap and ends when the ball is clearly in flight.

3. Straight out of the NBA Casebook:
RULE 4 - SECTION XI

46. Player A1 is fouled just as he is completing his dribble and gathering the ball. If he continues his shooting motion and scores a successful basket, how many free throws are awarded?

Since the player’s shooting motion continued and he was fouled upon gathering the ball, the basket shall count and Player A1 will receive one free throw attempt.