My arms and hands are getting dark?What shall i do?

The same think is happening to me, it is known as tanning. The best way to get the essential Vitamin D is through exposure to the sun and your skin cells are contributing to your health. What tanning does is to protect the chromosomes of the exposed skin cells to reduce the risk of serious chromosome damage that can, yes, lead to skin cancer. So, if for some reason you have spent weeks, months, or years out of the sun, take exposure slowly to prevent sun burning and literally the peeling off a layer of your skin. I am an immunologist and toxicologist by training, BTW.

Not worry about what is, after all, a completely natural reaction to sunlight?

Try to avoid the sun because that's probably why. Every time you go outside bring an umbrella with you for you wont become more darker.