Antiderivatives plus piecewise function

[JaysFanatic]

Hi.

Express F(x) when x> 1. $\displaystyle F(x) = \int_{0}^{x}f(t)dt$

where \(\displaystyle f(t) = \left\{\begin{array}{cc}t^{2}, \;\ t\geq 1 \\ 2-t, \;\ t\leq 1\end{array}\)

I had no idea how to start the problem. I thought maybe we had to take the anitderivative of $\displaystyle t^{2}$ to get $\displaystyle \frac{t^{3}}{3} + c$, but I'm not sure. Any help would be welcome!

 

[tkhunny]

That is correct. Now do the other piece, substitute x and 0, and solve the rest of the problem.