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there was a description:(Note that integral is a function only of t,so I use a total derivative (d/dt) in the first expression,but the integrand is a function of x as well as t , so it's a partial derivative in the second one (∂/∂t) )

so this text book started very simple and intuitive, but now I'm really confused.First of all why did d/dt appear and why did it "transform" to a partial derivative as it "entered" the integral?