Scheme and let syntax

 (define (Int开发者_如何学编程egral f a b N)  
    ;define h as a constant
    (let((h (/ (- b a) N))))       
     (define (Term n)   
      (* (/ h 3) (+ (* 2 (f (+ a (* 2 (* n h)))))   
            (* 4 (f (+ a (* 2 (* (- n 1) h)))))  
            )  
     ))  
     (+ (* (/ h 3) (+ (f a) (f b))) (sum Term a next (/ N 2.0))))  

This code produces an error r5rs:body: no expression in body in: (r5rs:body) Could you please help?

You misplaced the braces after the let. After you defined a constant in let the code that uses the constant has to be inside of the let's scope. Hence your error about missing the body of the expression.

Here is the corrected code:

(define (Integral f a b N)
  ; define h as a constant
  (let ((h (/ (- b a) N)))
    (define (Term n)
      (* (/ h 3) (+ (* 2 (f (+ a (* 2 (* n h)))))
                    (* 4 (f (+ a (* 2 (* (- n 1) h))))))))

    (+ (* (/ h 3) (+ (f a) (f b))) (sum Term a next (/ N 2.0)))))

BTW, you still need to define the sum function.