Explain briefly why the definite integral exists when f(x)= cases x^ 2 -9 x-3 , & x 3

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Explain briefly why the definite integral

\displaystyle\int_{1}^{5} f(x)\,dx

exists when

f(x)=\begin{cases}\dfrac{x^{2}-9}{x-3}, & x\neq 3,\\ \text{undefined}, & x=3. \end{cases}