simplifying expressions – Is simplify giving a “not always” correct answer here?

A result like this appears as one of the terms when I compute coefficients in a Fourier Series:

expr =(Sin(n*Pi))/((-4 + n^2))

If I simplify all my terms, this happens:

Simplify(expr, Assumptions -> Element(n, Integers)) (*returns a zero*)

Which is true except if n=-2 or 2:

Limit(expr, n -> 2) (*give Pi/4*)

Shouldn’t Simplify catching that?