Theorem: Integrable Function

If $f$ is continuous on $a,b$ or has a finite number of jump discontinuities on $(a,b),$ then $f$ is integrable on $a,b.$

Example $1$ Find the value of ${\displaystyle \underset{1}{\overset{4}{}}}(x^2-1)dx$ by evaluating a right Riemann sum and letting $n.$