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Using the public data from the Herschel wide field surveys, we study thefar-infrared properties of optical-selected quasars from the Sloan Digital SkySurvey. Within the common area of $\sim 172~deg^2$, we have identified thefar-infrared counterparts for 354 quasars, among which 134 are highly securedetections in the Herschel $250~\mu m$ band (signal-to-noise ratios $\geq5$).This sample is the largest far-infrared quasar sample of its kind, and spans awide redshift range of $0.14{\leq}z\leq 4.7$. Their far-infrared spectralenergy distributions, which are due to the cold dust components within the hostgalaxies, are consistent with being heated by active star formation. In mostcases ($\gtrsim80$\%), their total infrared luminosities as inferred from onlytheir far-infrared emissions ($L_{IR}^{(cd)}$) already exceed$10^{12}~L_{\odot}$, and thus these objects qualify as ultra-luminous infraredgalaxies. There is no correlation between $L_{IR}^{(cd)}$ and the absolutemagnitudes, the black hole masses or the X-ray luminosities of the quasars,which further support that their far-infrared emissions are not due to theiractive galactic nuclei. A large fraction of these objects($\gtrsim50\text{--}60\%$) have star formation rates $\gtrsim300~M_{\odot}yr^{-1}$. Such extreme starbursts among optical quasars, however,is only a few per cent. This fraction varies with redshift, and peaks at around$z\approx2$. Among the entire sample, 136 objects have secure estimates oftheir cold-dust temperatures ($T$), and we find that there is a dramaticincreasing trend of $T$ with increasing $L_{IR}^{(cd)}$. We interpret thistrend as the envelope of the general distribution of infrared galaxies on the($T$, $L_{IR}^{(cd)}$) plane.

Co-evolution of Extreme Star Formation and Quasar: hints from {\it Herschel} and the Sloan Digital Sky Survey