Given that $f$ satisfies $\left|f\left(u\right)-f\left(v\right)\right|\le \left|u-v\right|$ for u and v in $\left[a,b\right]\dot{}$ Then $\left|{\int }_a^{b}f\left(x\right)dx-\left(b-a\right)f\left(a\right)\right|\le$ (a)$\frac{\left(b-a\right)}{2}$ (b) $\frac{{\left(b-a\right)}^2}{2}$ (c)${\left(b-a\right)}^2$ (d) none of these

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