Derivative of an integral with both limits as functions of x?

[Asphyxiated]

Homework Statement

Find the derivative of:

$$\int_{tan(x)}^{2x^{2}} \frac {1}{\sqrt{1+t^{3}}} dt$$

Homework Equations

$$\frac{d}{dx} \int_{a}^{x} f(t) dt = f(x)$$

The Attempt at a Solution

I don't have an attempt because I do not know how to handle the problem... the FTC statement in 'Relevant equations' is only for the integral from a constant to a function of x, right? Help!

 

[fzero]

You can pick a constant and write that integral as the difference of two integrals, each of which only has a single limit that is a function of x.

 

[Unit]

Recall that the integral of f from a to b equals F(b) - F(a), where F' = f. Suppose there exists a function G(x) with the property that G'(x) = 1/(1+x^3). Don't forget the chain rule.