Kernels do not upgrade automatically to a next major version (like 3.13 to 3.16) through routine updates. You can do it manually by running

sudo apt-get install linux-generic-lts-utopic

You can read about HWE stack.

If you want to install graphical stack from Ubuntu 14.04.2, then you can run

sudo apt-get install --install-recommends linux-generic-lts-utopic xserver-xorg-lts-utopic libqt5gui5 libgles1-mesa-lts-utopic libgles2-mesa-lts-utopic libgl1-mesa-glx-lts-utopic libgl1-mesa-glx-lts-utopic:i386 libglapi-mesa-lts-utopic:i386 libegl1-mesa-drivers-lts-utopic

Here is a good guide for that.

The Ubuntu Wiki command can remove a lot of useful packages. In some cases it removes ubuntu-desktop. So it is not good to run it. Anyway be careful and look which packages are going to be removed before agree to proceed.

After you are happy with the new kernel, you can remove 3.13 kernel meta-packages to prevent 3.13 kernels from updating. It can be done by

sudo apt-get remove linux-image-generic linux-headers-generic

Also old kernel images and headers can be removed with Synaptic.

Update Now 3.19 kernel is available for Ubuntu 14.04. It can be installed by

sudo apt-get install linux-generic-lts-vivid