§5.1 Constructing accurate graphs of antiderivatives (continued)

Summary

A particle with $s(0) = 0.5$ has velocity graph enclosing $A_1 = \frac{7}{6}$ on $[0,1]$. Then $s(1)$ equals

The same particle's velocity is a downward parabola crossing zero at $t = 1$ and $t = 5$, positive between, negative outside. The position $s$ is

With velocity positive on $(0,1)$ and $(5,6)$ and negative on $(1,5)$, the position function $s$ is

Compute $s(1)$ as a fraction, given $s(0) = 0.5$ and the signed area $\frac{7}{6}$ accumulating over the first second.

A workout burns calories at piecewise constant rates, and the accumulation function $C$ satisfies $C(5) = 12.5$, $C(10) = 50$, $C(15) = 125$. Compute the calories burned between minute $5$ and minute $10$.

If $A(x) = \int_{-1}^{x}f(t)\,dt$ and $B(x) = \int_{0}^{x}f(t)\,dt$ with $\int_{-1}^{0}f(t)\,dt = 1$, then $A(x) = B(x) + 1$.