Definition (Definite Integral): Let be continuous on the closed interval

Second Fundamental Theorem of Integral Calculus: Let be continuous on the closed interval and let If is an anti-derivative of on then


Proof: By the First FTIC, on and since on we have on Finally, since are continuous on we have on for some constant What is Now, So, on In particular, 

Stated another way, the Second FTIC says