f:[0,pi]---R be defined by $\displaystyle f(x)=\sqrt sinx$

by considering the lower sum for the partition P={0,pi/6,5pi/6,pi},prove that $\displaystyle \int_0^{\pi}f\ge\sqrt2pi/3$

$\displaystyle I_1=[0,\pi/6]$, $\displaystyle d_1=\pi/6$

$\displaystyle I_2=[\pi/6,\pi*5/6]$, $\displaystyle d_2=\pi*2/3$

$\displaystyle I_2=[\pi*5/6,\pi]$, $\displaystyle d_3=\pi/6$

$\displaystyle L(f,P)=\sum_{i=1}^3m_id_i$ How do i find $\displaystyle m_i$ for each of the above interval.

Thanks