Studying the convergence of integral alone (ratio: zero/zero)

Question

I am looking for an examination of the convergence of the integral alone: $$\int_0^2 \frac {\sqrt{2-x}\,dx} {x^2-5x+6}$$

Any way to prove the convergence without calculation of the integral?

Answer 1

Hint: This integral is equal to $$\int_0^2\frac1{(3-x)\sqrt{2-x}}dx$$