(NOTE: I am using an example in my book, that I have the answer to already, because I want to understand how they arrived at the answer, that way, I can do the other problems on my own)

Okay, so here is the problem:

Approximate the area under the curve on the given interval usingnrectangles and the evaluation rules (a) left endpoint, (b) midpoint, and (c) right endpoint.

So, this is how the book solved this.....

y = x^{2}+ 1 on [0, 1] and n=16

(a) c_{i}= i∆x where i is from 0 to 15

A_{16}= ∆x (I do not know how to input the correct symbol here, but its 15 on top and i=0 on bottom) f(c_{i})

= 1/16 (that symbol again) [(i/16 + 1/16)^{2}+ 1]

(approximately =) 1.3652

Now, I sort of get how they get up to the last part, but I do not understand how they came to the conclusion of 1.3652. Any clarification on this would be greatly appreciated.