How to integrate with respect to a variable that was substituted?

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Take $P(x)=1000+\int_{0}^{x} M(s)ds$. If $x=5t$, how do I write an equation for the $P(x)$ as a function of $t$?

That is with the function being $P(t)$, not $P(5t)$. So how do I make $P(5t)=1000+\int_{0}^{t} M(s)ds$ into a $P(t)$ function?