Fundamental Theorem of Calculus Detail

Part One of the Fundamental Theorem of Calculus states that if $g$ is a continuous function on $[a,b]$ that is differentiable on $(a,b)$, and if $g'$ is integrable on $[a,b]$ then$$\int_{a}^{b}g'=g(b)-g(a)$$What I am wondering is: what does it mean that $g'$ is integrable on $[a,b]$? I reckon that it is necessary for the Theorem to hold, but I am not sure what the statement means by itself.