Let me say something from Math.
I read some answers,I can't say yes or no,because the Q is not clear.
I translate to Math:
If Intgral(p(t))from(0 to 60)=.9 , Find Int(p(t))from(0 to 10)?
The answer is not unique, .15 is too simple. 1-(.1)^(1/6) is understandable,I can say any p(t) culve ,monotonly not increase,...=.9,Int(p(t))from(0 to 10) could be answer by another meaning.