Maggie, a few things to consider:
First is that there is some difference in how "sensitive" cameras are for a scene exposure -- some tend to expose brighter or darker than others and you can see that as over- or under-exposing
Second, and this is important, you need to understand how the camera meter interprets a scene and uses that to set your exposure. The camera has several metering modes and uses that to measure the reflected light and then it interprets that light to be the tonal equivalent of "medium gray" and uses that interpretation to set the exposure. This is important, because even with the Evaluative Exposure mode the meter gives preference to the center of the image.
Now, if you look at the center of your image, you will note that it's occupied with a combination of blue sky and white, both of which are brighter than "medium gray". But the camera meter doesn't know that and so when the readding is done it interprets that center portion as the part of the image that should appear as gray and sets the adjustment accordingly so that, as you've seen, the image becomes more or less of a stop underexposed.
You can see this all the time by shooting say a bright sky or white snow. Look at the shots and they will be underexposed because of this. It's the way on-camera meters look. Like I say, some cameras have variations in sensitivity so some may seem to "compensate" for this better, but it still is a factor.
Now, as you've seen, when you are in P, Av or Tv using Exposure Compesation to adjust for this. You may be able to spot this when metering and "fix" it on the fly or, in the digital world, we have chimping which as you can see lets you spot a problem like this. But be aware that if you use EC in P, Av or Tv the camera will shift metering/exposure as you change the view but will not change the EC. The only way to confidently use the EC with those modes is to also learn how to use the Exposure Lock function when you need to or to be ready to change your EC on the fly. For example, with that scene if you metered on the center and adjusted it with EC then decided to reframe the shot so that the center of the book was off to the side and you were centered on the darker edge of the book, the meter would re-read and actually raise your "base" exposure but keep the EC set where you put it, so that in likelihood your image would now come out say a stop over-exposed! The two ways of dealing with that are to either press and hold the EC button before recomposing, or recompose then readjust your EC to, say the center.
Of course, I encourage people to also learn to shoot in Manual so that you take control of the exposure -- it is a very nice mode for a lot of shooting but you still need to learn to handle it in other modes as well.
