[tex]f''(\theta)=\sin\theta+\cos\theta[/tex]
Integrate both sides:
[tex]f'(\theta)=-\cos\theta+\sin\theta+C_1[/tex]
Integrate again:
[tex]f(\theta)=-\sin\theta-\cos\theta+C_1\theta+C_2[/tex]
With the given initial conditions, we find
[tex]f(0)=5\implies -1+C_2=5\implies C_2=6[/tex]
[tex]f'(0)=2\implies -1+C_1=2\implies C_1=3[/tex]
Then
[tex]f(\theta)=-\sin\theta-\cos\theta+3\theta+6[/tex]
