prove part (b) of this integration inequality

**(a)** Suppose that

is a continuous solution of

,

,

where

are continuous and

for

. Show that

,

.

This I have done! But then we have...

**(b)** Moreover, if

is increasing for

, show that

,

.

In order to do the exercise, we are given as a theorem the following formulation of the Gronwall inequality:

If

,

,

where

,

for all

and

is continuous, and

is a continuous solution, then

,

.

However, I believe this theorem may only be useful for part (a), which, as I said, I have already done. I provide it just in case.

Thanks in advance!