indefinite integral using trig functions. I am unable to solve this integration. i dont understand this integration py using trig identities. any help?

$$\int \frac{dx}{\sqrt{-x^2+25}} , \quad \frac{-\pi }{2}\le t\le\frac{\pi}{2}$$
use the substitution :$$x=5\sin t$$

and also my question is that what is $$\sqrt{-x^2+25}$$ in terms of $t$.

Its just a practise question.
Hint:

$$
\sqrt{25-x^2}=\sqrt{25-25 \sin^2 t}=5\sqrt{1-\sin^2 t}
$$

Now you can do it?
Let's compute

If $x=5\sin(t)$ then $dx=5\cos(t)dt$.

On the other hand,
 $$\sqrt{-x^2+25}=\sqrt{-{(5\sin(t))}^2+25}=\sqrt{-25\sin^2(t)+25}$$
by trig identities we find that $\sin^2(t)=1-\cos^2(t)$ so
 $$\sqrt{-25\cdot\sin^2(t)+25}=\sqrt{\ -25+{\cos t}^2 +25}=\cos(t)$$
I guess you'll be able to compute that integral.