Mathematics

Problem

Let

f: \mathbb{R} \to \mathbb{R}

be defined as

f(x) = \int_{0}^{x} (\sin^2 t + 1) dt

and

g

is the inverse function of

f

, then

g'\left(\frac{3\pi}{4}\right)

is equal to

\frac{p}{q}

, where

p, q

are coprimes, then

p + q

is equal to