GATE Civil Engineering (CE) 2014 Shift 2 Solved Paper

If {x} is a continuous, real valued random variable defined over the interval (− ∞, + ∞) and its occurrence is defined by the density function given as: $\mathit{f}\left(\mathit{x}\right)=\frac{1}{\sqrt{2\mathit{\pi }}\times \mathit{b}}\times {\mathit{e}}^{-\frac{1}{2}{\left(\frac{\mathit{x}-\mathit{a}}{\mathit{b}}\right)}^2}$where 'a' and 'b' are the statistical attributes of the random variable {x}. The value of the integral $\underset{-\mathit{\infty }}{\overset{\mathit{a}}{\int }}\frac{1}{\sqrt{2\mathit{\pi }}\times \mathit{b}}\times {\mathit{e}}^{-\frac{1}{2}{\left(\frac{\mathit{x}-\mathit{a}}{\mathit{b}}\right)}^2}\mathit{d}\mathit{x}$ is