If I have a Rectangle h high, b wide, I thought I could calculate 2nd Moment of Area, I , about its neutral axis this way: taking the top half of the rectangle, the area is bh/2, and then multiplying this by the distance from the centroid of the top half to the neutral axis, squared ie (h/4)**2. Then because there are two halves of the rectangle, doubling the answer. This all gives I=(bh**3)/16. My problem is reconciling this with the answer obtained by integrating (y**2) b dy from -h/2 to h/2, which gives I=bh**3)/12. I generally thought the concept of second moment of area was an area times the distance of the centroid of the area to an axis it is rotated about, squared. Now I'm not so sure. Any assistance appreciated.