# How do we get the canonical parameter $\theta$ from the exponential famility through the variance function?

The exponential family can be described by \begin{align*} f(y|\theta,\phi) = \exp\left\{\phi^{-1}(y\theta - b(\theta) + c(y,\phi)\right\} \end{align*}

It also can be shown that $$\textbf{E}(Y) = \mu = b^{\prime}(\theta)$$ and $$\textbf{Var}(Y) = \phi\ b^{\prime\prime}(\theta)$$. Based on this, we can define the variance function as $$V(\mu) = b^{\prime\prime}(\theta)$$. My question is: based on $$V$$, how do we recover $$\theta$$? The text which I am studying says that \begin{align*} \theta = \int V^{-1}(\mu)\mathrm{d}\mu \end{align*}

Although quite simple, I am having troubles in understanding this relation. Any help is appreciated. Thanks in advance!