Pull-back of 1-form

Question

Let $f : \mathbb{R} \rightarrow \mathbb{S}^1$ be the parameterization $f(\theta) = (\cos\theta, \sin\theta)$. If $\alpha$ is a 1-form on $\mathbb{S}^1$, prove that $$\int_{\mathbb{S}^1} \alpha = \int_0^{2\pi} f^*\alpha.$$ I know $$f^*\alpha(\theta) = (df_\theta)^*\alpha(f(\theta)),$$ but I'm not sure how to proceed.