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

• A. 1
• B. 0.5
• C. π
• D. 2 π