;; (list-of-areas F xmin xmax nsteps) produces the list of areas of rectangeles
;;    under the graph of the Function F
;; list-of-areas : Function Num Num Nat -> (listof Num)
;; requires : xmin less than or equal to xmax
;; Example :
(check-expect (list-of-areas (lambda (x) (+ (* x x) 1)) 2 4 4)
              (list 2.5 3.625 5 6.625))

(define (list-of-areas F xmin xmax nsteps)
  (map (lambda (x) (* x (/ (- xmax xmin) nsteps)))
       (map F (range xmin xmax (/ (- xmax xmin) nsteps)))))

;; (riemann-sum F xmin xmax nsteps) finds the area under the graph of Function F
;;    using Riemann Sums with nsteps steps between xmin and xmax
;; riemann-sums : Function Num Num Nat -> Num
;; requires : xmin less than or equal to xmax
;; Example :
(check-expect (riemann-sum (lambda (x) 3) 1 5 100) 12)

(define (riemann-sum F xmin xmax nsteps)
  (foldr + 0 (list-of-areas F xmin xmax nsteps)))

;; Tests :
(check-expect (riemann-sum (lambda (x) (+ (* x x) 1)) 2 4 4) 17.75)