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As shown by bbgodfrey , NIntegrate can solve your problem, but I just want to add, Integrate can actually handle InterpolatingFunction:

int[t_] = Integrate[y1[t] /. S1, t]

The output is an InterpolatingFunction representing the definite integral of $y_1(t)$ over $[0,t]$. The advantage of this approach is, you don't need to integrate again and again if you want to know the integral at other points. Just compare the following:

Table[int@t, {t, 0, 100, 1/10}]; // AbsoluteTiming
(* {0.015558, Null} *)
int2[tt_] := NIntegrate[y1[t] /. S1, {t, 0, tt}]
Table[int2@t, {t, 0, 100, 1/10}]; // AbsoluteTiming
(* {2.340323, Null} *)

Then

同学，如果你现在所获得的两个答案中的某一个真的帮到了你的话，你完全可以点一下你所满意的答案旁边的小勾（也就是上面那条评论里所说的Click the checkmark sign）来把它采纳（accept）了的。

As shown by bbgodfrey , NIntegrate can solve your problem, but I just want to add, Integrate can actually handle InterpolatingFunction:

int[t_] = Integrate[y1[t] /. S1, t]

The output is an InterpolatingFunction representing the definite integral of $y_1(t)$ over $[0,t]$. The advantage of this approach is, you don't need to integrate again and again if you want to know the integral at other points. Just compare the following:

Table[int@t, {t, 0, 100, 1/10}]; // AbsoluteTiming
(* {0.015558, Null} *)
int2[tt_] := NIntegrate[y1[t] /. S1, {t, 0, tt}]
Table[int2@t, {t, 0, 100, 1/10}]; // AbsoluteTiming
(* {2.340323, Null} *)

Then

同学，如果你现在所获得的两个答案中的某一个真的帮到了你的话，你完全可以点一下你所满意的答案旁边的小勾（也就是上面那条评论里所说的Click the checkmark sign）来把它采纳（accept）了的。

As shown by bbgodfrey , NIntegrate can solve your problem, but I just want to add, Integrate can actually handle InterpolatingFunction:

int[t_] = Integrate[y1[t] /. S1, t]

The output is an InterpolatingFunction representing the definite integral of $y_1(t)$ over $[0,t]$. The advantage of this approach is, you don't need to integrate again and again if you want to know the integral at other points. Just compare the following:

Table[int@t, {t, 0, 100, 1/10}]; // AbsoluteTiming
(* {0.015558, Null} *)
int2[tt_] := NIntegrate[y1[t] /. S1, {t, 0, tt}]
Table[int2@t, {t, 0, 100, 1/10}]; // AbsoluteTiming
(* {2.340323, Null} *)

Then

同学，如果你现在所获得的两个答案中的某一个真的帮到了你的话，你完全可以点一下你所满意的答案旁边的小勾（也就是上面那条评论里所说的Click the checkmark sign）来把它采纳（accept）了的。

As shown by bbgodfrey , NIntegrate can solve your problem, but I just want to add, Integrate can actually handle InterpolatingFunction:

int[t_] = Integrate[y1[t] /. S1, t]

The output is an InterpolatingFunction representing the definite integral of $y_1(t)$ over $[0,t]$. The advantage of this approach is, you don't need to integrate again and again if you want to know the integral at other points. Just compare the following:

Table[int@t, {t, 0, 100, 1/10}]; // AbsoluteTiming
(* {0.015558, Null} *)
int2[tt_] := NIntegrate[y1[t] /. S1, {t, 0, tt}]
Table[int2@t, {t, 0, 100, 1/10}]; // AbsoluteTiming
(* {2.340323, Null} *)

Then

同学，如果你现在所获得的两个答案中的某一个真的帮到了你的话，你完全可以点一下你所满意的答案旁边的小勾（也就是上面那条评论里所说的Click the checkmark sign）来把它采纳（accept）了的。

As shown by bbgodfrey , NIntegrate can solve your problem, but I just want to add, Integrate can actually handle InterpolatingFunction, in a quite fast way:

NIntegrate[y1[t] /. S1, {t, 0, 100}] // AbsoluteTiming
(* {0.015559, {1.17532*10^9}} *)
(int[t_] = Integrate[y1[t] /. S1, t]; int[100]) // AbsoluteTiming
(* {0., {1.17532*10^9}} *)

Then

同学，如果你现在所获得的两个答案中的某一个真的帮到了你的话，你完全可以点一下你所满意的答案旁边的小勾（也就是上面那条评论里所说的Click the checkmark sign）来把它采纳（accept）了的。

As shown by bbgodfrey , NIntegrate can solve your problem, but I just want to add, Integrate can actually handle InterpolatingFunction:

int[t_] = Integrate[y1[t] /. S1, t]

The output is an InterpolatingFunction representing the definite integral of $y_1(t)$ over $[0,t]$. The advantage of this approach is, you don't need to integrate again and again if you want to know the integral at other points. Just compare the following:

Table[int@t, {t, 0, 100, 1/10}]; // AbsoluteTiming
(* {0.015558, Null} *)
int2[tt_] := NIntegrate[y1[t] /. S1, {t, 0, tt}]
Table[int2@t, {t, 0, 100, 1/10}]; // AbsoluteTiming
(* {2.340323, Null} *)

Then

同学，如果你现在所获得的两个答案中的某一个真的帮到了你的话，你完全可以点一下你所满意的答案旁边的小勾（也就是上面那条评论里所说的Click the checkmark sign）来把它采纳（accept）了的。