need help in understanding a probably basic integration concept

I was reading a presentation on Ito's process. I read the following.

dx = a(x,t)dt

x(t) = x(0) + intgration from 0 to t (a(x,s))ds

What I do not understand is from where did 's' come and what is 's'? I think I have forgotten the basics of integration.

Thank you for your help.

Re: need help in understanding a probably basic integration concept

The s is a "dummy" variable. If you have function f(x) any anti-derivative is or , etc. It doesn't matter what you call the variable inside the integral.

For example,

They are all the same.

Re: need help in understanding a probably basic integration concept