Definite Integration

Let f : R \(\to\) R be a differentiable function such that \(f\left( {{\pi \over 4}} \right) = \sqrt 2 ,\,f\left( {{\pi \over 2}} \right) = 0\) and \(f'\left( {{\pi \over 2}} \right) = 1\) and

let \(g(x) = \int_x^{\pi /4} {(f'(t)\sec t + \tan t\sec t\,f(t))\,dt}\) for \(x \in \left[ {{\pi \over 4},{\pi \over 2}} \right)\). Then \(\mathop {\lim }\limits_{x \to {{\left( {{\pi \over 2}} \right)}^ - }} g(x)\) is equal to :