Given function $y(t)$, I am confused by the notation
$$x(t) = \int\limits_0^t y(\tau) d\tau$$
Can someone explain to me if $x(t)$ is a function of $t$, or the value evaluated at some $t$. Logically speaking, it should be a function, because when you plug in different $t$, you get different $x(t)$. But an integral is roughly a summation over infinitesimal intervals, so it is a number.
How do you distinguish between these two, notion-wise?