We now establish the fundamental connection between definite integrals and
antiderivatives (indefinite integrals). Let a continuous function f(t) be
defined for a0/t0/b and let x be any point inside the interval. Then if we regard a definite integral as a function of its upper limit, which we write as x ,
a function F (x ) may be defined as
F (x)g x
f (t) dt,
where t is a dummy variable.