TI83 computing LeftSum

METHOD 0 A program suggested by the textbook. This uses y1 for the function

PROGRAM RSUMS
:Disp "LOWER LIMIT"
:Input A
:Disp "UPPER LIMIT"
:Input B
:Disp "DIVS"
:Input N
:A->X
:0->S
:1->I
:(B-A)/N->H
:Lbl P
:S+H*Y1->S           ***** Y1 is via the vars menu and not just typed Y1
:X+H->X
:IS>(I,N)
:Goto P
:Disp "LEFT SUM"
:Disp S
:S+Y1*H->S
:A->X
:S-Y1*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