The question was to evaluate the integral of f(z) dz, around C, where C is the unit circle centered at the origin, using the general cauchy's theorem.

f(z) is 1/((2z^2)+1).

I know that f(z) is not analytic at i(sqrt2)/2 and -i(sqrt2)/2 and both points happen to be inside C, so cauchy's theorem can't be applied.

What's my next step?