From galactus,. It helped me verifying my result and confirmed it.$\displaystyle \frac{d}{dx}\int_{h(x)}^{g(x)}f(t)dt=f(g(x))g'(x)-f(h(x))h'(x)$

I got that thederivativeof $\displaystyle \int_a^{x^3} sin^3(t) dt=3x^2{sin(x^3)}^3$.

While from Mathematica, it gives the result $\displaystyle \frac{1}{12} \big (9cos(a)-cos(3a)-9cos(x^3)+cos(3x^3)\big)$ which I doubt is equal to my result. Can you confirm my result (if yes, I will think that the result from Mathematica is the same, even if it seems more than incredible.). Thanks!!