simplifying expressions - Simplify $cos(n pi)$ and $sin(n pi)$ when n is an integer

I was trying to calculate this integral in Mathematica 9:

2/π Integrate[ Cosh[a x] Cos[n x], {x, 0, π}, Assumptions -> n ∈ Integers]

I got as a result :

$$\frac{2 (a \sinh (\pi a) \cos (\pi n)+n \cosh (\pi a) \sin (\pi n))}{\pi \left(a^2+n^2\right)}$$

That's the same result I obtained manually, but how can I force Mathematica to change $\sin(n \pi)$ into $0$ and $\cos(n \pi)$ into $(-1)^n$ ?

Answer

Thanks to J. M. and Artes, I figured out what the problem was.

I had to change

2/π Integrate[ Cosh[a x] Cos[n x], {x, 0, π}, Assumptions -> n ∈ Integers]

into

Assuming[ n ∈ Integers, 2/π Integrate[ Cosh[a x] Cos[n x], {x, 0, π}]]

or

Simplify[ 2/π Integrate[ Cosh[a x] Cos[n x], {x, 0, π}], n ∈ Integers]

I don't know what's the problem with the first form but still, it works !