Let $\displaystyle g \in C^1$ such that g(0)=0 and g'(0)=1

$\displaystyle \phi(x)=\int g(t).dt$

upper limit: $\displaystyle log x$

lower limit: $\displaystyle x^2-1$

I have to calculate $\displaystyle \phi'$ and $\displaystyle \phi''$ and I have been reading about the fundamental theorem of calculus but I'm not too sure of how I can apply it to calculate $\displaystyle \phi'$ and $\displaystyle \phi''$. Every example I look at has some expression instead of just g(t) like I have.

(I apologize for not knowing how to put the limits in the integral.)

Thanks in advance.