(defun left-hand (a b n f)
  (declare (type double-float a b n)
           (ftype (function (double-float) double-float) f)
           (optimize (speed 3) (safety 1)))
  (do* ((dt (/ (- b a) n))
        (time a (+ time dt))
        (suma 0d0 (+ suma (the double-float (funcall f time))))
        (end (- b (/ dt 2))))
       ((> time end) (* dt suma)) (declare (type double-float suma dt))))


vs

(defun left-hand (a b n)
  (declare (type double-float a b n)
           (optimize (speed 3) (safety 1)))
  (do* ((dt (/ (- b a) n))
        (time a (+ time dt))
        (suma 0d0 (+ suma (the double-float (sin time))))
        (end (- b (/ dt 2))))
       ((> time end) (* dt suma)) (declare (type double-float suma dt))))