find integral of complex function using residues

Hello,

How can I find integral of a function like this: where I have to integrate with circle: . I MUST use residues to find the integral of this function. Maybe there is a simple, efficient way to do this?

Thank You in advance.

[David Goodmanson]

for the record,

integrand f(z) = (1/2) / (z^2+z/2-1)
               = (1/2) / ((z-r1)(z-r2))
r = roots([1 1/2 -1])
r = -1.2808
     0.7808
contour encloses positive root r(2)
residue = (1/2)*(r(2)-r(1))
Integral = (2*pi*i) * (1/2)*(r(2)-r(1)) = 0.0000 + 1.5239i