Tomyil... What he is saying is, if the limit is a CONSTANT.... Then the 't' is constant. So if u Differentiate it, you'll get 0 regardless of what u Differentiate it wrt.
However, since this is multivariable Calc,. While integrating the function wrt x, I think the t variable is TREATED as constant, and while it is being differentiated wrt t, t is treated as variable and X, if present, is constant.