Q:

Integration with Assumption, why doesn't it simplify?

I have a problem which surely someone else had on here, but in reading similar questions, I haven't found an answer. 
The problem is really trivial: 
Integrate[Sin[k*x]^2, {x, -Pi, Pi}, 
 Assumptions -> {k ∈ Integers}]

That shall simply give me
$$\pi$$
Because the whole result would be 
$$\pi -\frac{\sin (2 \pi  k)}{2 k}$$
But since $k\in\mathbb{Z}$ we have $\sin(2\pi k) = 0$ for every $k$.
Why doesn't mathematica print $\pi$ in the output, simply? 
P.s. Of couse "Elements" denotes the $\in$ symbol. Here something went wrong during the copy of the input text!

A:

Simplify is not automatically used
Assuming[{k ∈ Integers},
 Integrate[Sin[k*x]^2, {x, -Pi, Pi}] //
  Simplify]

(*  π  *)

