A derivative of an integral. Homework doubt

A derivative of an integral. Homework doubt

I need to solve this:
$$\frac{d}{dx}(\int_{0}^{x}\sqrt{t^2+1}dt)$$
So, first I solve the integral for $(0,x)$, only need to evaluate in $x$:
$$\frac{d}{dx}(\frac{x\sqrt{x^2}}{2}dt)$$
Then I solve the derivative:
$$\frac{d}{dx}(x^2dt)$$
Question
Is this the end?