Integral sum, splitting the interval into equal parts

I need to compile and calculate the function's $\displaystyle f(x) = sin x$ sum of the integral in interval $\displaystyle [0, \pi]$, while splitting the interval into $\displaystyle n = 6$ equal-length parts.

I do know how to do $\displaystyle \int_{0}^{\pi} sinx dx$, but how do I do this while splitting it in intervals?

I didn't attend lectures, so I'm stuck at easies parts (Worried)

can it look like this?

$\displaystyle \sum_{n=1}^{6}\int_{0}^{\pi} sinx dx$