The Star Formation History and Evolution of the Circumnuclear Region of M100

(Abridged) Star-forming nuclear rings in barred galaxies are common in nearby spirals, and their detailed study can lead to important insights into the evolution of galaxies, their bars, and their central regions. We present integral field spectroscopic observations obtained with SAURON of the bar and circumnuclear region of the barred spiral galaxy M100, complemented by new {\it Spitzer Space Telescope} imaging of the region. We use these data to enhance our understanding of the formation, evolution, and current properties of the bar and ring. We derive the kinematics of the gas and the stars and quantify circular and non-circular motions using kinemetry. We analyse this in conjunction with the optical and infrared morphology, and our previously published dynamical modelling. By comparing line indices to simple stellar population models we estimate the ages and metallicities of the stellar populations present within the region, especially in and around the ring. Our kinematic and morphological results all confirm the picture in which the nuclear ring in M100, considered typical, is fed by gas flowing in from the disc under the action of the bar, is slowed down near a pair of resonances, and forms significant amounts of massive stars. Detailed stellar population modelling shows how the underlying bulge and disc were put in place a number of Gyr ago, and that the nuclear ring has been forming stars since about 500~Myr ago in a stable succession of bursts. This confirms that nuclear rings of this kind can form under the influence of a resonant structure set up by a bar, and proves that they are stable features of a galaxy rather than one-off starburst events.