Verified answer

[tex]\displaystyle\bf\\u(t)=6+0,8t\\\\t_{1} =5 \ \ \ ; \ \ \ t_{2}=10\\\\\\S(t)=6t+0,8\cdot\frac{t^{2} }{2} =6t+0,4t^{2} \\\\\\S=S(t_{2} )-S(t_{1} )=6\cdot 10+0,4\cdot 10^{2} -(6\cdot 5+0,4\cdot5^{2} )=\\\\\\=60+40-30-10=60\\\\\\Otvet \ : \ S=60[/tex]