1its very easy
i can explain it to you via an illustration
EXAMPLE: ∫1+x dx
remember limit of a sum is just a way of approximation
Always remember the formula
∫ab f(x) dx= (b-a) limn→∞ 1/n [f(a) + f(a+h) +f(a+2h) +...f(a+(n-1)h)
where h=b-a/n
∫121+x dx =lim n→∞ 1/n [1+(1+1) + (1+2)+(1+3)+...(1+(n-1))
RHS=1+1+1...n times +(1+2+3+4+5+....(n-1 terms))
RHS =n+[(n-1)(n)/2]
The above was calculated using the sum of n natural numbers formula
RHS=take common n and then apply limit to get the answer
