How to prove $\int_{1}^{4} \sqrt{1+x^2} \, dx \geq 7.5$

Question

I need to prove that

$$\int_{1}^{4} \sqrt{1+x^2} \, dx \geq 7.5$$

but I can only use Integral Properties and the Riemann definition of the Definite Integral. I have tried calculating the integral but I always end up with nasty-looking terms inside the Riemann sum, even though I have tried different start and endpoints. Any help is appreciated.

Answer 1

$\textbf{Hint}$:

$$\sqrt{1+x^2} \geq x$$