How to differentiate this integral?

[jrsh]

Hello,

I have an integral

$$F(x) = \int\limits_a^x f(x) d(g(x))$$

and $$g(x)$$ may and may not be differentiable.

How can I differentiate $$d(F(x))$$?

Thanks

 

[HallsofIvy]

At points where g is differentiable F'(x)= f(x)g'(x). At points where g is not differentiable F is not differentiable.