Derivative of an integral $\sqrt{t}\sin t dt$ I need to find the derivative of this function. I know I need to separate the integrals into two and use the chain rule but I am stuck.
$$y=\int_\sqrt{x}^{x^3}\sqrt{t}\sin t~dt~.$$
Thanks in advance

Hint
By the chain rule we prove easly:
If 
$$F(x)=\int_{u(x)}^{v(x)}f(t)dt$$
then
$$F'(x)=f(v(x))v'(x)-f(u(x))u'(x)$$
