Answer
$i = 8.0~\mu A$
Work Step by Step
Note that the slope of each $B$ versus $t$ curve is $\frac{dB}{dt}$
We can find the induced emf:
$\mathscr{E} = -\sum A_i~\frac{d\Phi}{dt}$
$\mathscr{E} = -\sum A_i~\frac{dB_i}{dt}$
$\mathscr{E} = -(0.20~m)(0.10~m)~(\frac{4.0~\mu T/s}{2.0~s}+ \frac{2.0~\mu T/s}{2.0~s} -\frac{10~\mu T/s}{2.0~s})$
$\mathscr{E} = 4.0\times 10^{-8}~V$
We can find the magnitude of the induced current:
$i = \frac{\mathscr{E}}{R}$
$i = \frac{4.0\times 10^{-8}~V}{5.0~m\Omega}$
$i = 8.0~\mu A$
