I was asked to find the bounds of the integral $$\int_0^1 \frac{1}{\sqrt{4-x^2-x^3}}$$
that is . if
$\alpha \leq\int_0^1 \frac{1}{\sqrt{4-x^2-x^3}}\leq\beta$ I have to find $({\alpha}, {\beta)}$
that is so to do this, my book wrote:- $$\int_0^1\frac{1}{\sqrt{4-x^2}} \leq \int_0^1\frac{1}{\sqrt{4-x^2-x^3}} \leq \int_0^1\frac{1}{\sqrt{4-2x^2}}$$
however, these bounds seem arbitrary.
How to select bounds for such problems?