Reading the ming of a prof question

[transgalactic]

i was told that i would be asked a question that deals with
integrability and the link between the differentiability operation
and the integration operation(the basic laws of Newton calculus)

what question he can give that combines this things??
can you give an example??

i can't find a question like this

 

[Mark44]

i was told that i would be asked a question that deals with
integrability and the link between the differentiability operation
and the integration operation(the basic laws of Newton calculus)

what question he can give that combines this things??
can you give an example??

i can't find a question like this

Sounds like he might be thinking of the Fundamental Theorem of Calculus, which says in part for a suitable function f, that
$$\frac{d}{dx}\int_a^x f(t) dt = f(x)$$

Do a search on "fundamental theorem of calculus" and you should get some ideas.

$$\frac{d}{dx}\int_a^{x^2} f(t) dt = ?$$
Here's one fairly simple problem

Regarding "Newton calculus" both Isaac Newton and Gottfried Leibniz are credited about equally with the development of calculus.