Define domain and intervals of rising/falling

"Define domain and intervals of rising/falling of the following function f(x): $\displaystyle f(x)=\int_{0}^{x}\log(t^3+1)dt$."

__Domain__ of $\displaystyle f(x)$ is where $\displaystyle t>-1$: $\displaystyle (-1, \infty)$

What about function __falling/rising__ (assuming that I got the __domain__ right(Happy))? Isn't it so, that you just take derivative of f(x) and that "cancels" the integral, which would mean that f(x) is always rising for $\displaystyle t\geq 0$, because its derivative ($\displaystyle \log(t^3+1)$) is always positive with $\displaystyle t\geq 0$?