The odd numbers from 1 to 2001 are:

1, 3, 5, ........., 2001

This froms an AP

where first term a = 1

Common difference d = 3 - 1 = 2

last term l = 2001

Let number of terms = n

Now, l = a + (n - 1)d

=> 2001 = 1 + (n - 1)2

=> 2001 - 1 = (n - 1)2

=> 2(n - 1) = 2000

=> n - 1 = 2000/2

=> n - 1 = 1000

=> n = 1001

Now, sum = (n/2)*(a + l)

                = (1001/2)*(1 + 2001)

               = (1001/2) * 2002

              = 1001 * 1001

              = 1002001

So, the sum of odd integers from 1 to 2001 is 1002001