Applying Leibniz's Rule for Differentiating an Integral

[rootX]

Homework Statement

$$\int_{x}^{2\,{x}^{2}+1}sin{t}^{2}dt$$

I need to take differential of that

Homework Equations

Fundamental theorem of calculus

The Attempt at a Solution

I know 't' is a dummy var, so I replace it with x,

and then
get
sin((2x^2+1)^2)-sin(x^2)
as answer. But I am not very sure about my answer.

Can anyone please check my solution?

Thanks.

 

[Kreizhn]

Look up Leibniz's Rule. After that it's just a plug and chug:

Edit: Leibniz Rule, not Theorem