Here is what I was thinking
Let f be a constant function then
I just want to show that this equality can hold so I get
This gives two possible cases
either c=0 and a and b don't matter or
In either of these two cases equality holds so the statement is false.
Hmph. Chalk another one down to a mis-placed "not" in my brain. I knew in my head that the integrals were not, in general, equal. That means that the statement "These two integrals are not equal, in general" is itself true. There are situations when the integrals are equal, and other situations when they're not equal.