Answer: \(y=-\frac1{36}\sin\left(6x-\frac\pi2\right)+\frac{x}{3}+\pi\).

Integrate the second derivative:

So

At \(x=\frac{\pi}{4}\),

Since \(\cos\pi=-1\), and \(\frac{dy}{dx}=\frac12\),

\(\frac12=-\frac16(-1)+C.\)

Thus

\(C=\frac13.\)

Therefore

Integrate again:

The curve passes through \(\left(\frac{\pi}{4},\frac{13\pi}{12}\right)\). At this point, \(\sin\pi=0\), so

\(\frac{13\pi}{12}=\frac13\cdot\frac{\pi}{4}+A.\)

Hence

\(\frac{13\pi}{12}=\frac{\pi}{12}+A,\)

and therefore

\(A=\pi.\)

So the equation of the curve is