TI89 computing Left/Right Sum

You put the function into y1

Apps -> Program Editor -> New -> (enter the name in var field) rsums
You will be put in the middle of an editor make look like

rsums(a,b,n)
Prgm
Local x   ****** F4 then 3
a->x      ****** -> is the store
0->s      ****** zero not oh
0->i      ****** zero not oh
(b-a)/n->h
Lbl P
s+h*y1(x)->s
x+h->x
i+1->i
if i<n Then  **** F2 then If then If Then Endif
 Goto P
EndIf
Disp "left sum" **** F3 then Disp
Disp s
s+y1(x)*h->s
a->x
s-y1(x)*h->s
Disp "right sum"
Disp s

Test data y1=x^3, a=1, b=3, n=100 gives Left sum 19.7408 and right sum
of 20.2608