How to find the derivative of $F(t) = \int_0^t f(t, x) \, dx$?

How to find the derivative of $F(t) = \int_0^t f(t, x) \, dx$?

Let $f: \mathbb{R}^2 \to \mathbb{R}$ be a continuous function. Define $F:
\mathbb{R} \to \mathbb{R}$ by, $$ F(t) = \int_0^t f(t, x) \, dx $$ Then,
I'm not sure how to get $F'$. If, there are functions $g$ and $h$ such
that $f(t, x) = g(t)h(x)$, then of course we have $$ F(t) = \int_0^t f(t,
x) \, dx = \int_0^t g(t)h(x) \, dx = g(t)\int_0^t h(x) \, dx $$ which can
then be differentiated using the product rule. But apart from this special
case, I don't know how to get $F'$.