Find the sum of all integers 30 to 80, inclusive. (is there a formula to do this? )

Yes there is actually a formula for this. This is an arithmetic progression with a common difference of 1. 

The sum of terms can be solved by using the formula

S = (n/2) * (a1 + an)

where S is the sum of the terms
n is the number of terms 
a1 is the first term
an is the last term

we can calculate the number of terms, n by using the formula

an = a1 + (n-1)*d

d is the common difference equal to 1 

therefore n = 51

substituting to the first equation

S = 2805