Antiderivative of a Schwartz-function

Let  $\mathcal{S}(\mathbb{R})$  be the Schwartz-Space. Prove that if  $f \in \mathcal{S}(\mathbb{R})$  and  $\int_{-\infty}^\infty f(t)dt=0$, then there is  $F \in \mathcal{S}(\mathbb{R})$  such that  $f=F'$.

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