The given integral ∫f(x)dx can be transformed into another form by changing
the independent variable x to t by substituting x = g (t).
Consider I =∫ f x dx
Put x = g(t) so that `(dx)/(dt)` = g'(t)
dx = g′(t) dt
Thus I =∫f(x) dx ∫f ( g (t))g'( t) dt
This change of variable formula is one of the important tools available to us in the name of integration by substitution.