Continuity Implies Integrable

A function $f(x)$ is Integrable on a closed interval $[a,b]$ if:

• $f(x)$ is continuous on $[a,b]$
• $f(x)$ has a finite # of Jump Discontinuities on $[a,b]$ (Derived from Definite Integral) Derived from Fundamental Theorem of Calculus Part 1