Hello, Nichelle14 !
Didn't I solve this at another site?
Let $\displaystyle f(x) \;= \;\begin{Bmatrix}\frac{2}{\pi}x & 0 \leq x \leq \frac{\pi}{2} \\ 2\sin x & \frac{\pi}{2} < x \leq \frac{3\pi}{2} \\1 & \frac{3\pi}{2} < x \leq 2\pi \end{Bmatrix}$
a. Find a continuous function, $\displaystyle F(x)$, satifying $\displaystyle F(x) = \int^{2\pi}_0 f(t)\,dt$
b. Give the values of $\displaystyle x$ on $\displaystyle [0,\,2\pi]$ for which $\displaystyle F(x)$ is not differentiable.
c. Compute $\displaystyle \int^{2\pi}_0 f(x)\,dx$
On the interval $\displaystyle \left[0,\frac{\pi}{2}\right]$, the graph is a straight line.
On the interval $\displaystyle \left(\frac{\pi}{2},\,\frac{3\pi}{2}\right]$, we have a portion of the sine curve.
On the interval $\displaystyle \left(\frac{3\pi}{2},\,2\pi\right]$, the graph is a horizontal line.
The graph looks like this: Code:

1+ *
 * : * o * * * *
 * : * :
 * : * :
 *    +    *    +    +
 π/2 π* 3π/2 2π
 * :
 * :
1+ *
You should be able to answer the questions now . . .
.