Riemann sum for integral using subintervals

Question

I need to find the Riemann sum for the following integral, using a subdivison of the interval $[0,1]$ in 100 equally sized subintervals.

$f(t) = t^2 + t$

$\int_0^1 f(t) dt$

I a little stuck and was wondering, how this can be done.

Answer 1

If I understood your question correctly, you want the Riemann sum of $f(t)$ for the partition $P = \{0, 1/100, 2/100, ..., 99/100, 1\}$

This is, by definition: $$\sum_{i=1}^{100} f(c_i) \frac 1 {100}$$ where the $c_i$'s are each $\frac {i-1} {100} \le c_i \le \frac i {100}$.