1. An image-capturing device comprising: a plurality of imaging pixels for image generation, disposed along a first direction in a first row, each of the plurality of imaging pixels receiving a light flux corresponding to an image formed by an optical system on the image-capturing device; a plurality of focus detection pixels for a focus detection, which include a plurality of first focus detection pixels and a plurality of second focus detection pixels, disposed along the first direction in a second row in parallel to the first row, each of the plurality of first focus detection pixels receiving one of a pair of light fluxes passing through the optical system and each of the plurality of second focus detection pixels receiving an other of the pair of light fluxes; and an adder that adds a plurality of imaging outputs provided by a plurality of selected imaging pixels disposed according to a predetermined positional relationship with each other in the first row, selected from the plurality of imaging pixels to each other, a plurality of first focus detection outputs provided by a plurality of selected first focus detection pixels disposed according to a same positional relationship with each other in the second row as the predetermined positional relationship, selected from the plurality of first focus detection pixels to each other and a plurality of second focus detection outputs provided by a plurality of selected second focus detection pixels disposed according to the same positional relationship with each other in the second row, selected from the plurality of second focus detection pixels to each other, wherein the plurality of imaging outputs are each provided based upon the light flux received by each of the plurality of selected imaging pixels, and the plurality of first focus detection outputs and the plurality of second focus detection outputs are provided based upon the pair of light fluxes received by the plurality of selected first focus detection pixels and the plurality of selected second focus detection pixels.