Strange Integral Question (possbily parametric)

[Seeker555]

Find
\(\displaystyle \frac{d}{dx}\ \int \frac{sin(t^3)x}{t^2}dt\) - the upper boundary for the integral is \(\displaystyle 4+x^4\) and the lower is \(\displaystyle 2+cos^2(x)\)


I wouldn't even know what to search for to learn about this type of integral...

 

[galactus]

Do you mean \(\displaystyle \displaystyle \frac{d}{dx}\int_{2+cos^{2}(x)}^{4+x^{4}}\frac{sin(t^{3})}{t^{2}}dt\)?.

This is an exercise in the Second Fundamental Theorem of Calculus, but I must say, it appears rather unusual.

Note that:

\(\displaystyle \displaystyle \frac{d}{dx}\int_{g(x)}^{h(x)}f(t)dt=f(g(x))g'(x)-f(h(x))h'(x)\)

Can you finish?.