Of course there will be a group of over-achievers who finish at least Calc I in high school. I think finishing the college equivalent of Calc II (Integral Calculus) in high school is a stretch. Maybe...
Yet that was regarded as the norm here in Britain when I did my maths A-level back at the end of the 70s. I don't know about the whole of 'calculus II*', but we were expected to have at least a good grasp of Integral calculus and be able to symbolically integrate expressions of real variables of reasonable complexity and know how to do numerical integration. As I've said, the dividing line between 'school' and 'university' seemed to be drawn just before you started doing differential equations.
To give you a flavour of what was expected, here's half a question from a maths A-level
** paper from 1980 that's
here I've rendered half of one question here in mathjax to save folks from having to download and read that.
Here's the first of two parts of question 7. This is the easy part, part (b) is harder but I am not taking the time to render that into mathjax, it's way too long - see the pdf if you're curious.
7 (a) It is known that, for any integer \$k\$, \$\int^\pi_{-\pi} sin(k x) dx = 0, \text{and} \int^\pi_{-\pi} sin(k x) dx = \begin{cases}
2\pi & if k = 0 \\
0 & if k \neq 0
\end{cases}\$
Using the above results, show that if \$m, n\$ are positive integers,
(i) \$\int^\pi_{-\pi} sin(m x) cos(n x) dx = 0\$
(ii) \$\int^\pi_{-\pi} sin(m x) sin(n x) dx = \begin{cases}
\pi & if m = n \\
0 & if m \neq n
\end{cases}\$
(iii) \$\int^\pi_{-\pi} cos(m x) cos(n x) dx = \begin{cases}
\pi & if m = n \\
0 & if m \neq n
\end{cases}\$
* A bit of a foreign concept to a Brit, this uniform naming of undergraduate course units (and similar content between institutions) wasn't a 'thing' at British universities. At least, not in my day - I don't know about now.
** A-levels are the school examinations that Brits take at age ~18, covering material that was studied from ages ~17-18.