Corollary 8.4.7If
is integrable on
, then
is also integrable on
and
.

For definite integrals, the method of substitution (v.s. 2.2) is described as follows:

Theorem 8.4.8Let
be two numbers such that
Let
be a function having a continuous first derivative on
and such that
. If
is a function, continuous on the interval
, then for any
we have: