Proof of Ito's Identity using Ito's formula

Question

Prove $\int_{0}^{t} W_s dW_s=1/2 {W_t}^2-1/2t$ using Ito's formulas.

I don't really know how to approach this problem since I'm not given a function to find it's derivatives and plug into the Ito's formula which is:

$Y_t=f(0,0)+\int_{0}^{t}[\frac{df}{dx}(s,W_s)]dW_s+\int_{0}^{t}[\frac{df}{dt}(s,W_s)+\frac{1d^2f}{2dx^2}(s,W_s)]ds$

If I was given some function what I would do is:

1. Find partial derivatives required,
2. Plugin into the formula
3. Play about with it until I get the required

Answer 1

Here, Page $45$, example 4.1.3.