Let $M$ be a smooth manifold and let $\gamma: M \rightarrow M$ be a diffeomorphism. We denote by $\mathcal{A}(M)$ the algebra of differential forms. Let $f: \mathbb{R} \rightarrow \mathcal{A}(M)$ be a smooth map. Suppose that $\int\limits_0 ^ {+\infty} f(t)dt$ iis a well defined differential form.
Does the following equality hold
$$ \gamma^*\left(\int\limits_0 ^ {+\infty} f(t)dt\right) = \int\limits_0 ^ {+\infty} \gamma^* (f(t)) dt ? $$