Tomatoes.........

The integration process is the reverse of differentiation.

since (X)(1+X2)-1/2 is the derivateive of your function f(x) = sqr(1+x^2) then as it is in the integration formula it will produce the antiderivative ..i.e the function from which (X)(1+X2)-1/2 came out as derivative.....this is what we call indefinite integral or antiderivative.......the dx which accompanies the integral form is the so called differential of the variable x and it is compalsory to put it there....why? it is difficult to explain...

have a look here to understand a little bit about the differentials....

Differential of a function - Wikipedia, the free encyclopedia

Actually we integrate differentials........

MINOAS