The definition of definite integral 1. Y = x ^ 2 + 1 is integrable on [a, b]. Divide [a, b] n equally into ξ K (k is the subscript) (k = 1.2.3.4... N) the right end point of the cell is a + K (B-A) / N. how do you get the right end point? What does K (B-A) mean? 2. Why is LIM (n → + ∞) {B-A / n [n (a ^ 2 + 1) + B-A / N2a (1 + 2 +... N) + (B-A) ^ 2 / N ^ 2 (1 ^ 2 +... + n ＾ 2)] equal to (B-A) [a ^ 2 + 1 + AB-A ^ 2 + (B-A) ^ 2 / 3]?

The definition of definite integral 1. Y = x ^ 2 + 1 is integrable on [a, b]. Divide [a, b] n equally into ξ K (k is the subscript) (k = 1.2.3.4... N) the right end point of the cell is a + K (B-A) / N. how do you get the right end point? What does K (B-A) mean? 2. Why is LIM (n → + ∞) {B-A / n [n (a ^ 2 + 1) + B-A / N2a (1 + 2 +... N) + (B-A) ^ 2 / N ^ 2 (1 ^ 2 +... + n ＾ 2)] equal to (B-A) [a ^ 2 + 1 + AB-A ^ 2 + (B-A) ^ 2 / 3]?

1. When answering this question, we might as well take a look at the definition of integral and its geometric meaning
The value of K in the problem has been given. Substituting it into a + K (B-A) / N, we can get the following result:
a+(b-a)/n,a+2(b-a)/n,…… b. Taking K from 1 to N in turn is just the interval [a, b], and the interval is an equal interval. This shows that the above algebraic expressions are the right end of each equal interval. The expressions used in textbooks are different, but they have the same meaning. As for K (B-A), it just satisfies the corresponding equal interval when k is taken from 1 to n
2. I can't understand the second question