Given a function defined like this:
$$y(t) = \int_{-\infty}^t f(x) dx$$
(which i suppose is called parametric integral)
How can I calculate $y'(t)$ ?
I tried to take a look at this page and I found this formula:
$${d \over dx} \int_{f_1(x)}^{f_2(x)}g(t)dt = g(f_2(x))f_2'(x) - g(f_1(x))f_1'(x)$$
(which I suppose is one of the Leibniz integral rule) but I don't know if this can be applied to my case because the lower bound of the integral is indefinite.
HINT: assuming that the function is well defined then you have that
$$ \int_{-\infty }^t f=K+\int_{0}^t f $$
for $K:=\int_{-\infty }^0 f$. Then, if $f$ is continuous, you can apply the fundamental theorem of calculus. However if $f$ is not continuous at most you can apply Lebesgue's differentiation theorem.