The integral is $\"\"$ .

Theorem :

If $\"\"$ is integrable on $\"\"$ , then $\"\"$ ,

where width of the interval $\"\"$ , $\"\"$ number of subintervals and $\"\"$ .

Here $\"\"$ .

$\"\"$ .

Substitute $\"\"$ and $\"\"$ in $\"\"$ .

$\"\"$

The sum of $\"\"$ natural numbers is $\"\"$ .

The sum of squares of $\"\"$ natural numbers is $\"\"$ and $\"\"$ .

$\"\"$

$\"\"$ .