Here's the question you clicked on:
iplayffxiv
find the derivative
\[\frac{ d }{ dx }\int\limits_{0}^{x ^{3}}\sin t dt\]
\[=\frac{d}{dx} [-\cos(x^{3})-(-\cos(0))]\] \[= \frac{d}{dx} 1-\cos(x^{3})\] \[= 3x^{2} \sin(x^{3})\]
seems right to me. are you sure?
yes http://www.wolframalpha.com/input/?i=differentiate+integral+sin%28t%29+dt+from+0+to+x%5E3
i could not figure out how to type those limits in wolfram
so i had to ask it here