Evaluate the integral of a complex function over the unit circle

Question

Question: Evaluate $\int_{\gamma}(z^{3}+3)$ $dz$ where $\gamma$ is the unit circle centered at the origin described in positive sense

Is my approach right to this question okay?
I should determine the points where the integrand is not analytic like looking for zeros in my denominator
If this is correct then how do I set this up? I just learned this stuff and I only have notes on showing Cauchy Integral being analytic. Need help.

Update: On $\gamma$, if $z$=$e^{i\theta}$ then would that mean $dz$=$ie^{i\theta}$ $d\theta$ where $0\le \theta \lt 2\pi$
but incorporating this into the Cauchy formula is still not getting to me.

The formula is $f(z_0)$=$\frac{1}{2\pi i}\int_c \frac{f(z)}{z-z_0}$ $dz$
I am missing the key concept because I do not have a $z_0$ in my problem