simple question regarding frequency modulation (FM)
You may think that the bandwidth of an FM signal is \$2\Delta f\$, where \$\Delta f\$ is the frequency deviation (the maximum difference between the instantaneonus frequency \$f(t)\$ and the carrier frequency \$f_c\$).

However, the frequency of a signal cannot be changed in an instant, therefore when frequency modulating a carrier, you will introduce additional frequencies below \$f_c-\Delta f\$ and above \$f_c+\Delta f\$.

The bandwidth of a frequency modulated signal is theoretically infinite, but it can be approximated with the help of Carson's bandwidth rule (http://en.wikipedia.org/wiki/Carson_bandwidth_rule). It's an approximation based on the highest frequency in the modulating signal (\$f_m\$) and the frequency deviation. In your case, the deviation is 1 Hz and \$f_m\$ is 4 Hz, so the approximated bandwidth around the carrier is 10 Hz.