This Letter reports the first extraction of individual antineutrino spectra from ^{235}U and ^{239}Pu fission and an improved measurement of the prompt energy spectrum of reactor antineutrinos at Daya Bay. The analysis uses 3.5×10^{6} inverse beta-decay candidates in four near antineutrino detectors in 1958 days. The individual antineutrino spectra of the two dominant isotopes, ^{235}U and ^{239}Pu, are extracted using the evolution of the prompt spectrum as a function of the isotope fission fractions. In the energy window of 4-6 MeV, a 7% (9%) excess of events is observed for the ^{235}U (^{239}Pu) spectrum compared with the normalized Huber-Mueller model prediction. The significance of discrepancy is 4.0σ for ^{235}U spectral shape compared with the Huber-Mueller model prediction. The shape of the measured inverse beta-decay prompt energy spectrum disagrees with the prediction of the Huber-Mueller model at 5.3σ. In the energy range of 4-6 MeV, a maximal local discrepancy of 6.3σ is observed.
