Riemann integral

[guklu]

Hi, I was having some problem understanding these types of question on Riemann integrals (questions about 2 Riemann integrable functions and the Riemann integral of their combination). I have attached some photos below. Can anyone help me break down these 2 questions in simpler terms and how to go about starting them?

 

[pka]

I have been watching to see if anyone else had questions about the wording in this post.
@guklu, Will you please tell us if this is a professionally written question. That is, is it from a textbook or from a study guide?
I find it oddly written, in that it is hard to see what conditions are fixed and which vary from part to part.
Moreover, there is a clear typo in the very first question: the $\displaystyle dz$ is surely $\displaystyle dx$.
And I can see absolutely no reason to introduce $\displaystyle a<c<b$ and not use $\displaystyle c$.
Also if we are allowed to change $\displaystyle a~\&~b$ is seems easy to construct counter-examples.