Yes, it will be fine, and that build looks pretty good, except for one thing. Either get an aftermarket CPU cooler and a k-series CPU or a motherboard that can't be used for overclocking (your current CPU doesn't support overclocking but the board does).
Yes, all i5 CPUs have integrated graphics. And no, the GPU won't work together with integrated graphics; The integrated graphics won't be doing anything if you have a dedicated GPU.