diff --git a/scene/graph_scene.py b/scene/graph_scene.py
index 5caec9e6..1fde8684 100644
--- a/scene/graph_scene.py
+++ b/scene/graph_scene.py
@@ -245,6 +245,8 @@ class GraphScene(Scene):
                 sample_input = x
             elif input_sample_type == "right":
                 sample_input = x + dx
+            elif input_sample_type == "center":
+                sample_input = x + 0.5 * dx
             else:
                 raise Exception("Invalid input sample type")
             graph_point = self.input_to_graph_point(sample_input, graph)
@@ -421,6 +423,9 @@ class GraphScene(Scene):
 
         return group
 
+    def get_animation_integral_bounds_change(self):
+        pass
+
     def animate_secant_slope_group_change(
         self, secant_slope_group,
         target_dx=None,