I don't think there's a faster way with the information you've been given. You just have to be fast with finding areas of triangles and rectangles (and trapezoid/trapezium) and seeing when certain things cancel each other out.
Now, if you'd been given the start position (call it a) and end position (call it b), then there would be an easier way. It would be (1/14)(b-a). (By the fundamental theorem of calculus.)
Edit: You could however eliminate B immediately, since there's no way a denominator of 14 could get simplified to 16. You could eliminate E by eyeballing it. But I don't see easy ways to eliminate C and D.