How these two steps in Fourier transform are equal?

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Step1: (limit $Δs$ tends to $0$) (Summation $n=1$ to $\infty$) $\cos(nΔs(t-x)) Δs$

Step2 (Integration from $0$ to $\infty$) $\cos(s(t-x)) ds$

How is Step1 equal to Step2?