integration the very concept so i was just taught about integration and one thing i do not understand is that say we integrate x dx from 1 to 2 ... there are an infinite number of numbers between them ... so how does the sum turn out to be finite ?

Integration has got nothing to do with adding up numbers, let alone all numbers between two bounds which would be clearly impossible. It is rather about computing the area of the region bounded by the curve of the function, the $x$-axis, and the two vertical lines defined by $x=1$ and $x=2$.

This computation can be done by considering the limit of a sum of rectangle areas whose width gets smaller and smaller (and this point of view is called Riemann integration), but you should not fall in the trap of thinking like a physicist (with "infinitesimal rectangles of width $dx$") if your goal is to study maths.
