Complex Analysis: Sums of elementary fractions

[Potage11]

I have a homework question that reads:
Represent the following rational functions as sums of elementary fractions and find the primitive functions ( indefinite integrals );

(a) f(z)=z-2/z^2+1

But my confusion arrises when I read sums of elementary fractions.
I think what the question is asking is, show that it is holomorphic, in order to use the property g'(z)=f(z).

Could someone clarify this maybe?

 

[Gib Z]

It just means that as a whole, $$\int \frac{z-2}{z^2+1} dz$$ may be a hard integral, but $$\int \frac{z}{z^2+1} dz -2\int \frac{1}{z^2+1} dz$$ are 2 easy ones.