so i was to evaluate the integral of (x^2 + 5x + 3)dx with an upper limit of 5 and a lower limit of 1 using the definition of the integral (sorry I don't know how to do the notation on here)

I got dx = 4/n

lim n->infinity summed from i=1 to n [(1+ (4i/n))^2 + 5(1+(4i/n)) + 3)(4/n)

this simplified to lim n->infinity summed from i=1 to n [(112i)/(n^2) + (64i^2)/(n^3) + 36/n)

this is equal to lim n->infinity [(112/n^2)((n(n+1))/2) + ((64n)(n+1)(2n+1))/(6n^3) + (n)(6/n)]

when I simplified and evaluated the limit I ended up with 250/3 ... am I close? Thanks for the help guys